UNIVERSITY  OF  CALIFORNIA   PUBLICATIONS 

IN 

AGRICULTURAL    SCIENCES 

Vol.  4,  No.  8,  pp.  183-232,  1 1  figures  in  text  May  20,  1921 


THE  TEMPERATURE  RELATIONS  OF  GROWTH 
IN  CERTAIN  PARASITIC  FUNGI* 


BY 

HOWAED  S.  FAWCETT 


CONTENTS 

PAGE 

Introduction  184 

Methods 193 

The  culture  medium  193 

Stock  cultures ..  195 

The  experimental  cultures  195' 

Observations  on  growth 196 

The  maintained  temperature  chambers  198 

Structural  differences  related  to  temperature 198 

The  experimental  data 199 

Discussion  of  results 204 

General  considerations  ., 204 

The  growth  temperature  graphs 206 

Changes  in  the  growth  temperature  relations  210 

Comparison  of  growth  temperature  relations  of  different  organisms  by 

means  of  graphs  brought  to  the  same  height  211 

Eelation  of  growth-rate  to  the  time  of  exposure  214 

Temperature  coefficients 217 

Introductory 217 

Temperature  coefficients  in  the  present  study 220 

Conclusion 229 

Literature  cited  231 


*  Paper  No.  62  from  the  University  of  California,  Graduate  School  of  Tropical 
Agriculture  and  Citrus  Experiment  Station,  Eiverside,  California.  Manuscript 
submitted  September  2,  1919. 


184  University  of  California  Publications  in  Agricultural  Sciences        [Vol.4 


INTRODUCTION 

It  is  commonly  recognized  that,  of  the  many  different  and  varying 
conditions  that  affect  life  processes,  temperature  is  one  of  the  most 
important.  The  range  of  temperature  at  which  certain  important 
physiological  processes  may  occur  at  all  is  relatively  narrow,  and 
comparatively  slight  temperature  changes  produce  marked  effects  upon 
the  velocity  of  other  processes  having  more  extended  ranges.  Although 
many  biological  investigators  recognized  the  great  importance  of  this 
subject,  the  more  detailed  study  of  the  effects  of  maintained  temper- 
atures on  vital  processes  awaited  the  development  of  simple,  adequate 
and  inexpensive  methods  of  artificial  temperature  control.  In  the 
earlier  investigations  of  temperature  effects  upon  organisms  it  was 
often  impossible  to  maintain  the  desired  constant  temperature  through- 
out sufficiently  long  periods  of  time  to  get  results  that  might  be  con- 
sidered as  related  to  maintained  temperatures.  In  recent  years  a 
rapidly  increasing  number  of  papers  reporting  investigations  on  the 
effects  of  maintained  temperatures  upon  different  physiological  pro- 
cesses is  an  indication  that  more  attention  is  now  being  given  to  this 
subject.  There  is  still,  however,  a  great  lack  in  our  knowledge  in  this 
field,  especially  as  regards  plants.  On  certain  animal  processes  some- 
what more  work  appears  to  have  been  done,  though  even  in  this  field 
much  remains  to  be  accomplished. 

It  should  be  remembered  in  this  connection,  also,  that  the  subject 
of  the  temperature  responses  in  living  things  involves  problems  more 
complicated  than  those  just  suggested  as  having  to  do  with  maintained 
temperatures.  Most  organisms  (aside  from  warm-blooded  animals) 
are  never  exposed,  in  nature,  to  maintained  temperature  for  any  con- 
siderable period  of  time;  their  temperature  environment  is  practically 
always  in  a  state  of  flux.  From  this  it  follows  that  a  knowledge  of 
the  relation  holding  between  maintained  temperatures  and  vital  pro- 
cesses, no  matter  how  thorough  such  knowledge  may  be,  can  not  be 
expected  to  be  a  complete  basis  for  an  interpretation  of  physiological 
processes  going  on  under  natural  conditions.  In  order  to  obtain  a 
more  adequate  basis  for  such  an  interpretation  suitable  methods  need 
to  be  devised  for  dealing  also  with  rate  of  temperature  change  as  an 
environmental  condition,  aside  from  the  degree  of  temperature  itself. 
The  experimental  aspect  of  this  phase  of  physiological  and  ecological 


1921]   Faivcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      185 

temperature  relations  remains  practically  untouched  as  yet.  It  is 
almost  unmentioned  in  the  literature  as  a  serious  consideration,  al- 
though MacDougal  (1914)  has  called  attention  to  its  great  importance. 
It  is  clear,  at  any  rate,  that  the  problem  of  temperature  influence 
upon  organisms  falls  readily  into  two  fundamentally  related  but  super- 
ficially different  portions,  one  dealing  with  maintained  temperature 
and  the  other  with  fluctuating  temperatures.  Practically  all  the  con- 
trolled experimental  work  hitherto  published  deals  with  the  first  por- 
tion of  the  problem,  and  it  is  in  this  same  category  that  the  present 
investigation  lies.  Indeed  it  seems  unwise  to  attack  the  problems 
related  to  fluctuating  temperature  until  a  more  thorough  appreciation 
has  been  gained  concerning  the  general  principles  underlying  the 
influence  of  maintained  temperatures  upon  vital  processes.  It  was 
with  the  aim  of  throwing  additional  light  on  some  of  the  principles 
underlying  the  effects  of  maintained  temperatures  on  the  growth  of 
certain  fungi  that  the  investigation  reported  in  this  paper  was  under- 
taken. 

Filamentous  fungi  were  used  because  they  are  comparatively  simple 
organisms  whose  growth  rate  may  be  easily  measured,  because  they 
lend  themselves  readily  to  culture  in  darkness  and  because,  each  cell 
being  in  direct  contact  with  all  features  of  its  environment,  their 
relation  to  their  surroundings  is  simple  and  close.  The  four  forms — 
Pytlnacijstis  citrophthora  Smith  and  Smith,  Phytophthora  terrestria 
Sherbakoff,  Phomopsis  citri  Fawcett  and  Diplodia  natalensis  Evans — 
were  used,  all  of  them  being  parasitic  on  citrus  trees.  These  were 
known  to  grow  well  on  certain  prepared  media  and  some  evidence  was 
at  hand  showing  that  they  differed  from  one  another  as  regards  their 
temperature  relations. 

Another  reason  for  selecting  these  four  citrus  parasites  was  the 
possibility  that  their  pathogenic  activities  might  be  influenced  by 
climatic  temperature  conditions.  It  was  thus  possible  that  a  study 
of  their  temperature  relations  might  throw  some  light  upon  their 
probable  occurrence  and  upon  methods  of  combating  them.  General 
observations  in  connection  with  many  diseases  due  to  plant  parasites 
have  indicated  that  temperature  is  a  very  important  factor  in  their 
prevalence  in  any  given  season  or  in  any  given  region.  N.  E.  Stevens 
(1917)  has  shown  that  the  rate  of  increase  in  diameter  of  chestnut 
blight  cankers  is  closely  related  to  temperature.  Edgerton  (1915) 
has  emphasized  the  apparent  relation  of  temperature  conditions  to 
the  occurrence  of  certain  plant  diseases  in  subtropical  climates.     He 


186  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

is  convinced  that  the  absence  of  anthracnose  in  beans  grown  at  certain 
seasons  in  Louisiana  is  due  to  the  fact  that  the  average  temperatures 
for  the  seasons  when  the  disease  is  absent  are  too  far  above  the  opti- 
mum for  the  growth  of  the  pathogenic  fungus.  The  writer  (1917) 
has  previously  referred  to  the  limited  geographical  distribution  of 
melanose  due  to  Phomopsis  citri,  one  of  the  fungi  here  studied,  and 
has  suggested  that  temperature  conditions  may  be  among  the  important 
factors  limiting  its  distribution.  Humphrey  (1914)  came  to  the  con- 
clusion that  temperature  differences  in  various  localities  in  the  state 
of  Washington  largely  determined  the  differences  in  distribution  and 
severity  of  the  tomato  wilt  induced  by  Fusarium  oxysporum.  Tisdale 
(1917)  has  shown  for  Fusarium  wilt  of  flax  that  the  temperature  at 
which  the  host  is  most  injured  by  the  disease  corresponds  to  that 
favoring  the  maximum  growth  of  the  parasite  in  cultures. 

For  many  parasitic  organisms  it  is  probable  that  the  temperature 
range  within  which  serious  infection  of  their  hosts  may  occur  natur- 
ally is  comparatively  small.  Temperature  differences  and  differences 
in  moisture  conditions  may  largely  account  for  many  of  the  striking 
differences  observed  in  the  occurrence  of  many  plant  diseases  from 
season  to  season  and  from  one  region  to  another.  Many  other  obser- 
vations aside  from  those  given  above  might  be  mentioned  in  this  con- 
nection, but  it  seems  to  be  clear  enough  that  the  pathological  or 
agricultural  point  of  view  demands  much  more  thorough  knowledge 
than  we  yet  have  concerning  the  temperature  relations  of  parasitic 
fungi.  It  was  thus  thought  that  the  results  obtained  in  the  present 
study  might  ultimately  be  of  value  in  pathological  work. 

Considering  the  limited  time  available  for  this  study,  it  appeared 
better  to  confine  the  experimentation  to  the  four  forms  mentioned 
above  and  to  subject  the  results  to  a  critical  study  than  to  include  a 
larger  number  of  forms,  with  the  accompanying  necessity  of  treating 
the  results  in  a  more  superficial  manner.  Our  knowledge  regarding 
the  physiology  of  fungi,  as  well  as  that  regarding  plant  temperature 
relations,  may  be  increased  first  by  intensive  studies  of  a  few  forms. 
After  the  main  principles  have  been  worked  out  for  certain  selected 
forms  it  may  become  largely  a  matter  of  routine  to  compare  a  large 
number  of  organisms  with  respect  to  the  principles  previously  worked 
out.  The  four  fungi  here  to  be  considered  seemed  to  offer  oppor- 
tunities for  intensive  study,  and  they  also  furnish  valuable  material 
for  comparisons. 


1921]    Fawcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      187 

As  naturally  follows  from  the  general  concept  of  conditional  con- 
trol of  physiological  processes  (Verworn,  1912),  the  relation  of  the 
process  studied  to  any  given  condition  is  determined  not  only  by  the 
given  condition  but  also  by  the  remaining  conditions.  For  example, 
if  the  temperature  relations  of  a  given  organism  are  to  be  dealt  with 
they  must  necessarily  be  stated  together  with  as  definite  a  description 
as  possible  of  the  non-temperature  conditions  that  are  supposed  to  be 
effective.  To  state  that  the  mycelial  mat  of  a  given  fungus  was  ob- 
served to  enlarge  more  rapidly  at  one  temperature  than  at  another 
means  little,  unless  it  be  also  stated  just  what  sort  of  medium  was 
employed ;  just  what  was  the  length  of  the  time  period ;  just  what 
relation  this  time  period  had  to  the  beginning  of  the  test ;  just  what 
the  radiation  conditions  were,  etc.  By  altering  the  non-temperature 
conditions  the  relations  of  a  given  process  to  different  maintained 
temperatures  may  be  profoundly  altered.  To  illustrate  still  more 
concretely:  Lehenbauer  (1914)  found  that  the  optimum  temperature 
for  elongation  of  the  shoots  of  maize  seedlings  in  his  experiments  was 
30°  C.  when  the  exposure  period  was  6  hours,  and  the  corresponding 
optimum  temperature  for  an  exposure  period  of  12  hours  was  32°  C. 
If  Lehenbauer 's  twelve-hour  period  of  exposure  be  divided  into  four 
periods  of  three  hours  each,  and  if  the  optimum  temperature  be  calcu- 
lated from  his  data  for  each  of  these  four  successive  periods  separately, 
the  optima  are  found  to  be  30°,  31°,  31°,  and  32°  C.  respectively. 
Obviously,  any  physiological  process  must  be  regarded  as  controlled 
by  all  the  effective  conditions  acting  together.  The  conditions  that 
influence  the  rate  of  growth  of  a  fungus  in  a  culture  may  be  roughly 
classified  in  five  groups  as  follows: 

(1)  The  nature  of  the  fungus,  which  implies  its  internal  condi- 
tions— everything  that  goes  to  make  it  the  particular  organism  that 
it  is.  This  set  of  internal  conditions  is  vaguely  and  partially  indi- 
cated by  the  name  of  the  fungus,  with  an  implied  morphological  con- 
cept of  its  form  and  development,  to  which  the  name  refers.  But  it 
is  well  known  that  the  same  species  of  fungus  may  develop  quite 
different  complexes  of  internal  characteristics  under  different  sets  of 
environmental  conditions.  For  this  reason  it  is  of  the  greatest  im- 
portance to  include  not  merely  a  morphological  description  but  defi- 
nite information  concerning  the  previous  history  of  the  experimental 
organisms. 

(2)  The  nature  of  the  medium,  implying  all  the  physical  and  chem- 
ical properties  of  the  space  about  the  hyphae,  their  environment.    For 


188  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

the  most  part,  the  conditions  of  the  medium  (aside  from  temperature 
and  radiation)  involve  the  concentration  of  numerous  chemical  sub- 
stances such  as  oxygen,  carbon  dioxide,  starches,  sugars,  acids,  inor- 
ganic salts,  etc. 

(3)  Temperature  conditions.  Since  the  temperature  of  the  hyphae 
follows  closely  that  of  the  medium  and  since  the  latter  follows  closely 
the  temperature  of  the  more  distant  surroundings  of  the  culture,  it  is 
conventional  to  consider  the  temperature  of  these  surroundings  as 
constituting  a  condition  in  itself.  After  all,  however,  it  is  the  tem- 
perature of  the  fungus  hypha  that  directly  influences  its  rate  of 
growth,  not  that  of  the  medium,  culture  dish  or  chamber  about  the 
dish,  etc.  But,  since  the  temperature  of  all  these  spaces  is  practically 
the  same,  this  last  distinction  has  generally  been  ignored.  The  tem- 
perature conditions  for  two  cultures  may  differ  in  several  ways.  If 
they  are  maintained  temperatures,  they  may  differ  in  degree  or  in- 
tensity alone,  and  we  may  express  them  in  terms  of  degrees  on  some 
thermometer  scale.  If  they  are  not  maintained  temperatures,  they 
may  differ  (a)  as  to  the  particular  temperatures  with  which  the  cul- 
tures were  started,  ( b )  as  to  the  direction  of  variation  during  a  given 
period  (whether  the  temperature  became  higher  or  lower  with  time), 
and  (c)  as  to  the  time  rate  of  temperature  variation.  It  is  clear  that 
this  rate  of  change  in  temperature  may  itself  be  constant,  or  may  vary 
throughout  a  given  time  period.  When  only  maintained  temperatures 
are  to  be  considered,  as  in  the  present  study,  the  only  differences  to  be 
dealt  with  between  any  two  cultures  are  those  of  degree  or  intensity 
as  measured  in  terms  of  centigrade,  etc.,  degrees. 

(4)  Radiation  conditions,  involving  the  various  groups  of  wave- 
lengths of  radiation  and  the  relative  and  absolute  intensities  of  each 
group.  Up  to  the  present  time  most  biological  discussion  has  ignored 
most  of  the  wave-lengths  of  radiation  excepting  the  small  group  com- 
monly designated  as  light.  Since  the  cultures  of  the  present  study 
were  uniformly  carried  out  in  darkness  and  in  chambers  around  which 
a  mass  of  water  was  continuously  circulating,  radiation  conditions 
will  not  require  attention  here. 

(5)  The  duration  condition,  implying  the  length  of  time  during 
which  the  organism  is  subjected  to  the  other  conditions.  From  one 
point  of  view  every  condition  has  a  duration  factor,  but  when  most 
of  the  conditions  are  maintained,  or  practically  so,  the  duration  factor 
is  common  to  all,  and  we  may  regard  it  as  a  separate  condition.  More- 
over, as  far  as  the   presenl    investigation  is  concerned,  this  duration 


1921]   Fawcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      189 

condition  may  be  divided  into  two  parts,  each  one  of  which  may  be 
considered  as  a  separate  condition:  (a)  the  actual  length  of  any 
interval  of  time  considered,  and  (b)  the  location  of  this  time  interval 
in  the  entire  culture  period  reckoned  from  its  beginning.  If  the  time 
period  be  always  reckoned  from  the  beginning,  the  second  aspect  of 
the  duration  condition  may  be  neglected  and  only  the  length  need  be 
considered,  as  is  done  in  the  first  part  of  the  discussion  of  the  present 
investigation.  When,  however,  changes  in  rate  of  growth  are  studied 
with  reference  to  the  age  of  the  culture,  the  location  of  the  observation 
period  within  the  culture  period,  as  well  as  its  length,  come  to  be 
important,  and  these  may  be  regarded  as  two  different  duration  con- 
ditions, as  is  done  in  the  latter  part  of  the  discussion  to  follow. 

To  illustrate  all  these  conditions  in  detail,  a  certain  fungus,  Pythi- 
acystis  (condition  1)  is  surrounded  by  nutrient  agar  (condition  2), 
and  subjected  to  a  maintained  temperature  of  23°  C.  (condition  3), 
in  darkness  (condition  4),  and  it  exhibits  an  average  growth  rate  of 
8.0  mm.  per  day  for  a  period  of  three  days  after  inoculation  (con- 
dition 5). 

In  the  example  just  given,  the  observation  period  begins  with  the 
beginning  of  the  culture  period.  An  observation  period,  however, 
need  not  begin  with  the  beginning  of  the  culture  period  and  may  not 
be  continued  to  the  end  of  the  culture  period.  Thus  two  observation 
periods  may  be  alike  in  length,  say  two  days,  but  they  may  still  have 
entirely  different  relations  to  the  beginning  of  the  culture  period,  so 
as  to  constitute,  in  a  sense,  distinct  duration  conditions.  Of  course, 
this  state  of  affairs  is  to  be  related  to  changes  that  go  on  within  the 
organism,  with  the  lapse  of  time,  even  though  all  physical  and  chem- 
ical environmental  conditions  are  assumed  to  be  maintained  without 
alteration.  The  organism  is  generally  not  exactly  the  same  at  the 
moment  of  inoculation  of  a  culture  as  it  is  a  day  later,  four  days  later, 
etc.  This  consideration  introduces  one  of  the  most  perplexing  features 
of  the  whole  study  of  maintained  temperatures  as  related  to  vital 
processes,  and  considerable  attention  will  be  devoted  to  it  in  the  later 
sections  of  this  paper. 

From  the  points  mentioned  in  the  preceding  paragraphs  it  is,  of 
course,  clear  that  no  very  definite  knowledge  of  the  various  environ- 
mental influences,  as  they  act  to  control  the  physiological  processes 
of  any  organism,  may  be  expected  from  physiological  tests  in  which 
any  of  the  effective  conditions  are  allowed  either  to  vary  or  to  differ 
in  unknown  ways.     As  long  as  the  conditions  differ  only  in  known 


190  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

ways  from  one  culture  to  another,  or  as  long  as  they  vary  only  in 
known  ways  in  the  same  culture,  there  is  hope  of  advancing  our 
knowledge  of  environmental  influences. 

In  order  that  the  inoculum  for  each  series  should  be  as  similar  as 
possible  to  that  of  any  other  series,  the  four  species  were  kept  in  the 
dark  in  stock  tube  cultures  with  ordinary  corn-meal  agar  and  at  a 
temperature  ranging  from  about  16°  to  18°  C.  From  these  primary 
stock  cultures  inoculations  were  made  at  frequent  intervals,  on  agar 
plates  of  the  same  kind  of  medium  and  kept  at  the  above  temperature 
range.  These  plates  formed  the  secondary  stock  cultures.  The  mar- 
ginal region  of  a  mycelial  disk  of  a  secondary  stock  culture  (about  five 
days  after  inoculation)  furnished  material  for  inoculating  the  experi- 
mental cultures  of  that  fungus.  The  inocula  for  each  species  were 
fairly  similar,  therefore,  with  respect  to  parentage,  age,  vegetative 
activity,  etc.  Practically  the  same  amount  of  inoculating  material 
was  always  transferred  to  each  experimental  culture.  It  is  conse- 
quently safe  to  suppose  that  all  experimental  cultures  of  the  same 
fungus  were  practically  alike  at  the  beginning,  no  matter  when  they 
were  made.  The  four  fungi  used  furnish,  for  the  whole  study,  four 
different  sets  of  initial  complexes  of  internal  genetic  conditions.  Pro- 
gressive variation  in  the  internal  conditions  of  the  fungus  is  one  of 
the  features  taken  into  consideration  and  will  receive  attention  in  later 
sections. 

Although  several  different  media  were  employed  in  certain  aspects 
of  the  experimentation,  only  one  (corn-meal  agar)  will  be  considered 
in  the  present  paper.  Special  precautions  were  taken  to  have  this 
medium  as  nearly  as  possible  the  same  at  the  beginning  of  all  cultures, 
no  matter  at  what  time  they  were  started.  The  consistency  of  results 
obtained  by  repetition  showed  that  this  aim  was  practically  attained. 
It  was  also  shown  by  special  tests  on  one  of  the  fungi  (Pythiacystis) 
that  the  unoccupied  medium  did  not  considerably  alter  during  the 
period  of  any  single  culture.  It  therefore  seems  safe  to  suppose  that 
the  medium  was  always  the  same  at  the  beginning  of  all  cultures,  and 
also  that  the  medium  remained  practically  unaltered  during  the  pro- 
gress of  any  culture,  at  least  until  it  was  reached  and  passed  by  the 
enlarging  weft  of  hyphae.  Unquestionably  the  medium  occupied  by 
the  mycelial  disk  suffered  alterations  in  composition,  but  it  was  not 
apparenl  that  such  changes  influenced  the  rate  of  growth  of  marginal 
hyphae. 


1921]   Fawcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      191 

Since  the  elongating  hyphae  lie  largely  near  the  aerial  surface  of 
the  agar  plate,  while  some  are  partially  in  contact  with  the  air  space 
above,  it  is  well  to  consider  the  aerial  environmental  conditions,  as 
well  as  those  within  the  agar  medium  itself.  Aside  from  temperature, 
the  air  conditions  in  the  culture  dishes  above  the  agar  were  sensibly 
the  same  in  all  cultures  at  the  start,  except  that  the  pressure  of  water 
vapor  was,  of  course,  different  for  cultures  exposed  to  different  tem- 
peratures. Since  the  air  space  of  the  culture  dish  was  always  practi- 
cally saturated  with  water  vapor,  the  pressure  of  the  water  vapor 
would  nearly  follow  the  equilibrium  vapor  pressure  of  water  at  the 
various  temperatures.  The  unsealed  dishes  allowed  a  slow  escape  of 
water  vapor  and,  consequently,  a  slow  evaporation  from  the  agar  sur- 
faces during  the  culture  period,  the  rate  of  water  loss  being  somewhat 
greater  at  higher  than  at  lower  temperatures.  Different  maintained 
temperatures,  therefore,  were  automatically  accompanied  by  slightly 
different  rates  of  variation  in  the  water  content  of  the  yet  unoccupied 
medium.  Such  variation  may  be  neglected  in  this  case,  however,  since 
it  was  shown  by  special  tests  that  variations  even  larger  than  those 
that  actually  occurred  in  the  experimental  cultures  had  no  appreciable 
influence  on  the  rates  of  growth  of  the  fungi. 

As  has  been  said,  the  temperature  conditions  were  always  artifi- 
cially maintained,  with  a  very  small  degree  of  fluctuation  throughout 
any  given  culture  period.  The  radiation  conditions  are  regarded  as 
nonexistent  in  these  tests.  Light  (and  radiation  of  still  shorter  wave- 
lengths) was  always  excluded  and  the  stirring  apparatus  operated  to 
prevent  any  one-sided  action  of  long-wave  radiation  upon  the  cultures. 

The  duration  condition  offers  no  particular  difficulty  in  such  work 
as  this.  Since  the  experimental  cultures  are  all  regarded  as  alike  at 
the  time  of  inoculation,  the  duration  conditions  may  be  regarded  as 
beginning  to  operate  from  the  beginning  of  this  culture  period,  the 
time  of  inoculation  being  considered  as  zero  time.  If  either  the  length 
of  the  culture  period  or  the  time  between  observations  for  any  culture 
is  different  from  that  for  another,  this  fact  is,  of  course,  quantitatively 
shown  by  the  inoculation  intervals  between  successive  observations. 

From  the  preceding  discussion  it  will  be  observed  first  that  the 
research  at  hand  was  so  planned  as  to  involve  the  actual  or  assumed 
control,  during  the  respective  culture  periods,  of  all  the  groups  of 
effective  conditions  except  internal  ones,  and  second,  that  the  only 
conditions  considered  as  effectively  different  from  culture  to  culture 


192  University  of  California  Publications  in  Agricultural  Sciences        [Vol.4 

are:  (1)  the  nature  of  the  fungus  used  (initial  internal  conditions), 
(2)  the  rate  and  direction  of  physiological  alteration  within  the 
organism,  and  (3)  maintained  temperature. 

The  following  scheme  may  serve  to  show  the  sorts  of  terms  that 
enter  into  the  interpretative  comparisons  that  may  be  made  for  an 
investigation  of  this  kind : 

A.  COMPARISON  OF  CULTUEES  OF  THE  SAME  FUNGUS 

I.  Internal  conditions  (genetic  constitution  and  physiological  state  of  fungus). 

1.  Initial  conditions,  alike  for  all  cultures  of  same  fungus. 

2.  Direction  and  rate  of  physiological  alteration  during  culture  period,  may 

be  different  from  one  set  of  cultures  to  another.     This  alteration  always 
to  be  stated  as  within  the  limits  prescribed  by: 

(a)  The  initial  internal  conditions,  and 

(b)  The  external  conditions. 
II.  External  conditions  (environment). 

1.  Initial  environmental  conditions,  except  temperature,  considered  alike  for 

all  cultures  of  same  fungus. 

2.  Initial  temperature  conditions  different  from  one  set  of  cultures  to  another 

set. 

3.  All  environmental  conditions  assumed  to  be  maintained  at  their  initial 

values  throughout  the  culture  periods. 

B.  COMPARISON  OF  CULTURES  OF  DIFFERENT  FUNGI 

I.  Internal  conditions  (genetic  constitution  and  physiological  state  of  fungus). 

1.  Initial  internal  conditions  different  for  four  different  fungi. 

(a)  As  to  genetic  constitution    (whose  capabilities  are  roughly  indi- 
cated by  taxonomic  description). 

(b)  As  to  physiological  state,  because  of  different  reaction  of  different 
fungi  to  essentially  identical  preliminary  environmental  conditions. 

2.  Direction  and  rate  of  physiological  alteration  during  culture  period,  may 

be  different  from  culture  to  culture.     This  variation  always  to  be  stated 
as  within  the  given  limits  set  by  the  initial  internal  conditions  and  the 
external  conditions,  as  above. 
II.  External  conditions  (environment). 

1.  Initial  environmental  conditions,  except  temperature,  considered  alike  for 

all  cultures. 

2.  Initial  temperature   conditions   either  alike  or   different   from   culture   to 

culture. 

3.  All  environmental   conditions  assumed  to  be  maintained  at  their  initial 

values  throughout  the  culture  periods. 

The  study  here  reported  is  thus  seen  to  comprise  five  different 
studies.  The  influence  of  maintained  temperatures  on  the  growth  rate 
of  i'i\c\\  of  four  fungi  was  measured,  under  the  given  non-temperature 
conditions,  which  are  considered  as  initially  alike,  and  under  the  given 


1921  ]    Fawcett:  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      193 

initial  internal  conditions  also  considered  as  alike  for  all  cultures  of 
the  same  fungus.  The  fifth  study  comprises  the  comparison  of  the 
four  fungi  as  to  their  temperature  relations  under  the  given  set  of 
non-temperature,  external  conditions. 

The  investigation  reported  in  the  present  paper  was  carried  out 
during  the  period  between  October,  1916,  and  June,  1918,  in  the  labor- 
atory of  Plant  Physiology  of  the  Johns  Hopkins  University.  The 
author  wishes  to  express  his  thanks  to  Dr.  H.  .J.  Webber  and  the 
University  of  California  for  arrangements  that  made  it  possible  for 
him  to  be  absent  from  the  Citrus  Experiment  Station  during  the 
period  just  named.  He  also  wishes  to  record  his  appreciation  of  the 
privileges  and  facilities  accorded  him  by  the  Johns  Hopkins  University, 
including  a  Johnston  scholarship  in  that  institution.  Finally,  he 
desires  to  acknowledge  his  indebtedness  to  Professor  B.  E.  Livingston 
and  to  Dr.  H.  E.  Pulling,  of  the  laboratory  of  Plant  Physiology  of 
the  Johns  Hopkins  University,  for  much  valued  aid  and  criticism  in 
connection  with  the  planning  and  carrying  out  of  the  experimental 
part  of  this  study  and  in  the  interpretation  and  presentation  of  the 
results. 


METHODS 
The  Culture  Medium 

The  corn-meal  agar  employed  in  these  experiments  was  prepared 
according  to  the  procedure  described  by  Shear  and  Wood  (1912), 
using  20  gm.  of  corn  meal  and  15  gm.  of  agar  shreds  for  each  liter  of 
water.  More  water  was  added  before  the  final  filtering,  so  that  there 
was  one  liter  of  the  medium  for  each  20  gm.  of  corn  meal  originally 
used. 

The  exact  chemical  and  physical  nature  of  such  a  culture  medium 
can  not,  of  course,  be  stated.  It  undoubtedly  contains  a  large  number 
of  inorganic  salts  and  a  still  larger  number  of  organic  compounds,  all 
in  rather  low  concentration.  It  also  contains  various  substances  in  a 
state  of  suspension,  and,  since  it  has  more  or  less  the  nature  of  a  gel, 
there  is  no  marked  tendency  for  these  to  precipitate  out.  Since  the 
time  available  for  this  study  was  limited,  it  was  decided  to  make  no 
attempt  to  devise  a  nutrient  medium  of  known  composition  or  even  to 
find  out  what  any  of  the  media  commonly  employed  by  mycologists 


194  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

may  contain.  In  order  to  be  able  to  proceed  immediately  to  the  prob- 
lem of  temperature  influence,  the  whole  matter  of  nutritional  condi- 
tions— a  very  important  one  in  itself — was  ignored.  All  that  was 
done  in  this  connection  was  to  be  sure  that  the  medium  employed 
would  support  what  appeared  to  be  excellent  growth  of  all  four  fungi, 
and  to  take  precautions  so  that  practically  the  same  medium  might 
always  be  used  throughout  the  entire  study.  Since  corn-meal  agar 
is  an  infusion  of  corn  meal  and  agar-agar  shreds,  both  of  them  ex- 
ceedingly complicated,  unknown,  and  variable  materials,  it  was  feared 
that  different  samples  of  the  medium  might  be  very  different.  And 
an  attempt  was  made  to  avoid  this  danger  by  preparing  enough  medium 
at  the  beginning  for  the  entire  investigation,  mixing  it  thoroughly 
in  a  single  container  and  then  preserving  it  in  bottles  for  future  use. 
That  the  infusion  itself  might  alter  with  time  was,  of  course,  possible, 
but  various  repetitions  of  the  experiments  indicated  clearly  that  such 
alteration — if  it  occurred — was  not  of  such  nature  and  magnitude  as 
to  alter  the  growth  of  the  fungi  when  other  conditions  were  the  same. 
Since  the  amount  of  medium  necessary  for  the  entire  study  could 
not  well  be  prepared  in  a  single  day,  about  eight  liters  *were  made  at 
a  time,  until  about  48  liters  were  ready.  The  entire  amount  was  then 
liquefied  by  heat,  placed  in  a  20-gallon  earthenware  vessel  and  thor- 
oughly mixed,  after  which  it  was  poured  into  liter  bottles.  The 
mouths  of  the  bottles  were  then  plugged  with  cotton  in  the  usual  way 
and  the  bottled  medium  was  immediately  subjected  to  a  temperature 
of  115°  C.  for  15  minutes.  This  heating  was  repeated  on  the  two 
following  days,  after  which  the  tops  of  the  cotton  plugs  were  flamed 
and  covered  with  several  thicknesses  of  paraffined  paper,  tied  tightly 
around  the  bottle  neck.  The  bottles  of  medium  were  stored  in  dark- 
ness at  a  temperature  of  about  18°  C.  "When  a  lot  of  cultures  were 
to  be  made  the  required  number  of  bottles  of  medium  were  removed 
from  storage,  brought  into  the  liquid  condition  by  heating  in  the  auto- 
clave, and  used  in  the  ordinary  way  for  pouring  the  plates.  About 
15  c.c.  of  medium  was  used  in  each  culture  dish.  It  was  found  by 
test  that  this  amount  might  be  increased  or  diminished  by  as  much  as 
3  c.c.  or  more  without  perceptibly  influencing  the  growth  of  the  fungi. 


1921]    Faircett :  Temperature  'Relations  of  Growth  in  Certain  Parasitic  Fungi      195 


STOCK  CULTUEES 

The  original  sources  of  the  fungus  materials  were  as  follows: 
Pythiacystis  citrophthora,  isolated  by  the  author  from  the  diseased 
bark  of  a  lemon  tree  suffering  from  gummosis,  at  Whittier,  California, 
in  August,  1915 ;  Phytophthora  terrestria,  also  isolated  by  the  author 
from  the  diseased  bark  of  a  citrus  tree  suffering  from  mal  di  gomma, 
at  Palmetto,  Florida,  in  January,  1914;  Diplodia  natalensis,  isolated 
(by  Mr.  J.  M.  Rogers)  from  a  citrus  tree  in  the  Isle  of  Pines,  W.  L, 
and  received  by  the  writer  in  the  fall  of  1916 ;  and  Phomopsis  citri, 
received  from  H.  E.  Stevens,  from  Florida,  in  October,  1916.  All 
four  fungi  had  been  cultivated  under  the  same  conditions,  in  tubes 
of  corn-meal  agar,  in  darkness  at  from  16°  to  20°  C,  for  at  least  nine 
months  previous  to  the  beginning  of  the  experiment.  During  that 
time  transfers  to  new  tubes  of  media  had  been  made  at  intervals  of 
about  six  or  eight  weeks.  These  cultures  may  be  termed  the  primary 
stock  cultures  in  this  study.  The  four  fungi,  therefore,  had  each  been 
subjected  for  at  least  nine  months,  to  the  same  environmental  condi- 
tions. They  had  also  been  grown  in  the  same  kind  of  medium  as  that 
into  which  they  were  now  to  be  introduced  for  the  temperature  ex- 
periments. 

THE  EXPEEIMENTAL  CULTUEES 

Approximately  five  days  before  the  starting  of  each  series  of  ex- 
periments several  cultures  of  each  fungus  were  started,  by  transferring 
small  bits  of  medium  containing  mycelium  from  a  primary  stock  cul- 
ture to  the  center  of  the  agar  plates.  These  were  the  secondary  stock 
cultures,  and  were  kept  in  darkness  with  a  temperature  of  about 
20°  C.  for  about  five  days  previous  to  the  making  of  the  experimental 
cultures.  Little  plugs  or  disks  were  cut  out  of  the  agar  plate  just 
behind  the  advancing  margin  of  the  circular  growth  area  of  one  of 
these  five-day  secondary  stock  cultures.  The  disks  were  2.5  mm.  in 
diameter  and  about  1.5  mm.  thick.  They  were  cut  out  by  means  of  a 
cylindrical  platinum  cutting  device  like  that  described  by  Keitt  (1915) . 
Each  disk  was  lifted  on  the  flattened  end  of  a  platinum  needle  and 
was  then  inverted  and  placed  centrally  upon  the  surface  of  a  new 
agar  plate.  The  petri  dishes  used  were  10  cm.  in  diameter  and  1  cm. 
deep ;  each  contained  approximately  15  c.c.  of  corn-meal  agar,  which 
had  been  poured  hot  and  allowed  to  solidify  before  the  transfers  were 
made.    After  inoculation  the  experimental  cultures  were  divided  into 


196  University  of  California  Publications  in  Agricultural  Sciences        [Vol.4 

seven  similar  groups,  and  one  of  these  groups  was  placed  in  each  of 
the  seven  chambers  of  the  temperature-control  apparatus.  The  cul- 
tures of  any  given  species  always  occupied  the  same  relative  position 
in  all  the  chambers  and  in  all  the  series.  This  precaution  was  ob- 
served so  that  any  possible  difference  in  temperature  between  the 
upper  and  lower  portions  of  the  chamber  would  not  render  the  mea- 
surements of  the  different  lots  of  the  same  species  incomparable.  But 
such  differences  in  temperature  between  different  parts  of  any  one  of 
the  seven  chambers  proved  to  be  slight  (less  than  0.5°  C.  between  the 
top  and  bottom  of  a  chamber).  The  cultures  of  Pythiacystis  citroph- 
thora  and  Phytophthora  terrestria  occupied  a  position,  on  the  rack  in 
the  chamber,  at  nearly  the  same  level  as  the  bulb  of  the  thermometer 
from  which  the  temperature  records  were  taken.  The  cultures  of 
Phomopsis  citri  were  about  15  cm.  below  and  those  of  Diplodia  nata- 
lensis  were  about  15  cm.  above  the  thermometer  bulb  in  each  case. 


Observations  on  Growth 

As  the  hyphae  grew  out  in  all  directions  from  the  center  of  the 
plate  a  rounded  mat  or  mycelial  disk  was  formed  on  or  near  the 
surface  of  the  medium.  This  disk  remained  practically  circular,  as  it 
enlarged,  for  both  Pythiacystis  citroplithora  and  Phomopsis  citri, 
forming  a  nearly  perfect  circle  at  all  stages  of  enlargement.  The 
mycelial  disks  of  Diplodia  natalensis  and  Phytophthora  terrestria  were 
often  slightly  irregular  in  form  or  rather  evenly  lobed,  especially  at 
the  higher  temperatures  used.  No  irregularities  in  growth,  such  as 
bring  about  zonation  in  mycelial  mats  of  many  fungi,  were  observed 
in  any  of  the  cultures  with  maintained  temperatures.  In  special  tests, 
however,  in  which  the  fungi  were  grown  for  a  certain  time  in  one 
temperature  and  then  transferred  and  grown  in  a  markedly  different 
temperature,  such  zonation  was  pronounced. 

Observations  were  made  at  daily  intervals  for  a  culture  period  of 
from  four  to  six  days.  The  chief  matter  of  observation  was  the  mean 
diameter  of  the  disk,  which  was  obtained  by  averaging  two  measure- 
ments of  different  diameters,  selected  to  represent  the  disk  as  a  whole. 
When  the  margin  of  the  enlarging  disk  was  clear  and  definite  these 
measurements  were  made  by  menus  of  a  thin  millimeter  scale  applied 
on  the  bottom  of  the  Petri  disli  outside.  In  other  cases  the  Petri 
dishes  were  inverted  and  the  length  of  the  mycelial  outgrowth  was 
measured    by    means    of   a    microscope    with    an    ocular    micrometer. 


1921]   Faivcett:  Temperature  Eelations  of  Growth  in  Certain  Parasitic  Fungi      197 

Measurements  with  the  millimeter  scale  were  read  to  within  0.5  mm. 
This  was  deemed  sufficiently  precise  for  the  purpose. 

Since  none  of  these  fungi  produced  anything  but  vegetative  hyphae 
during  the  culture  periods  employed  and  the  growth  activities  were 
not  complicated  by  the  formation  of  any  reproductive  bodies,  these 
measurements  of  the  mycelial  disks  and  the  daily  increments  of  disk 
enlargement  derived  from  them  appear  to  furnish  as  satisfactory  a 
criterion  of  physiological  activity  in  general  as  might  be  found.  The 
only  other  criterion  for  such  comparisons  as  these,  and  that  hitherto 
generally  used  by  physiological  workers,  is  the  rate  of  production  of 
mycelium  measured  on  the  basis  of  dry  weight ;  the  employment  of 
this  criterion  offers  great  practical  difficulty  when  agar  medium  and 
short  culture  periods  are  used. 

At  the  time  of  observations,  each  chamber  was  opened  for  a  frac- 
tion of  a  minute  to  remove  just  one  group  of  cultures,  all  the  cultures 
being  alike.  These  dishes  were  immediately  wrapped  in  cotton  bat- 
ting, to  exclude  light  and  prevent  very  rapid  temperature  changes. 
Each  dish  was  removed  from  the  wrapping  for  a  minute  or  less,  while 
the  observations  were  made,  and  was  then  returned  to  the  wrapping. 
After  all  the  cultures  of  the  group  had  been  observed  the  entire  group 
was  replaced  in  its  temperature  chamber  and  another  group  was  taken 
out  for  observation.  The  time  required  for  the  entire  operation  of 
removing,  measuring,  and  replacing  a  group  of  10  cultures  averaged 
less  than  10  minutes. 

The  opening  of  the  chambers  for  removing  and  replacing  the  groups 
of  cultures  had  very  little  effect  upon  the  temperature  of  the  chamber 
itself.  The  thermographs  in  the  chambers  usually  showed  the  occur- 
rence of  this  series  of  momentary  openings  by  a  slight  rise  or  fall  of 
the  pen  tracing,  producing  short  vertical  lines,  each  representing  a 
degree  or  less  of  practically  momentary  alteration  in  the  temperature 
of  the  chamber. 

Several  tests  were  carried  out  to  determine  whether  the  daily  dis- 
turbance of  the  maintained  temperature,  caused  by  removing  the 
cultures  for  observation,  might  exert  any  appreciable  influence  on  the 
growth  of  the  fungi.  These  tests  showed  that  the  amount  of  growth 
observed  after  several  days  was  practically  the  same  whether  the  cul- 
tures had  been  left  in  the  chamber  for  the  whole  period  or  had  been 
removed  for  daily  observation  in  the  regular  way.  These  daily  dis- 
turbances of  the  maintained  temperature  are  considered  negligible  in 
the  present  study. 


198  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


The  Maintained  Temperature  Chambers 

The  various  temperatures  employed  in  the  experiments  here  consid- 
ered were  maintained  by  means  of  an  apparatus  described  by  Livings- 
ton and  Fawcett  (1920) .  This  apparatus  consisted  essentially  of  seven 
experiment  chambers  about  33  cm.  in  diameter  and  43  cm.  deep,  each 
one  surrounded  below  and  at  the  sides  by  a  large  mass  of  water.  Light 
was  excluded.  The  air  of  the  chamber  and  the  water  around  it  were 
kept  in  constant  circulation  by  mechanical  stirrers.  The  seven  cham- 
bers were  built  in  a  row,  with  the  water  jacket  of  each  in  contact  with 
that  of  the  next,  except  for  a  sheet-iron  partition  which  kept  the 
several  masses  of  water  entirely  separate.  A  tank  of  mechanically 
stirred  water  having  automatic  temperature  control  was  added  at  either 
end  of  the  series  of  experiment  chambers  and  the  entire  apparatus  was 
well  insulated  from  the  surroundings.  The  two  ends  of  the  series 
were  adjusted  for  any  two  desired  temperatures.  Between  these, 
after  equilibrium  had  been  established,  lay  the  maintained  temper- 
atures to  be  studied,  each  of  which  differed  from  the  next  by  a  certain 
amount,  depending  on  the  position  of  the  chamber  in  the  series.  The 
daily  fluctuations  in  any  chamber  were  only  rarely  more  than  0.5°  C. 
Access  to  the  chambers  was  had  from  above,  and,  of  course,  the  main- 
tained temperatures  of  the  cultures  were  slightly  disturbed  by  opening 
for  observations,  as  has  been  noted. 


STRUCTURAL  DIFFERENCES  RELATED  TO  TEMPERATURE 

Microscopic  observation  of  the  fungus  hyphae  near  the  margin  of 
the  mycelial  disk  was  made  occasionally,  at  the  time  of  measuring. 
Since  no  spores  were  produced  in  any  of  the  experimental  cultures  in 
the  time  here  recorded,  vegetative  growth  alone  can  be  considered. 
The  only  structural  differences  observed  between  different  cultures  of 
the  same  fungus  consisted  in  more  or  less  marked  peculiarities  in 
cultures  that  had  been  exposed  to  very  high  or  very  low  temperatures. 
Within  a  range  of  maintained  temperatures  extending  downward  about 
12  degrees  or  15  degrees  centigrade  below  a  temperature  slightly  above 
the  optimum  temperature  for  enlargement  no  influence  of  temperature 
on  structure  was  noticeable.  Within  this  range  the  hyphae  were  of 
regular  and  simple  form  and  the  branching  was  regular. 


1921]    Fawcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      199 

With  temperatures  near  the  maximum  point  at  which  any  enlarge- 
ment would  occur,  the  outgrowing  hyphae  were  of  irregular  shape, 
bent  and  twisted,  with  occasional  swellings  and  usually  with  apical 
enlargements.  The  hyphal  diameter  was  usually  much  larger  than 
that  of  hyphae  with  more  favorable  temperatures  for  enlargement, 
and  these  thicker  irregular  hyphae  showed  contents  that  appeared  dark 
colored  and  granular,  in  contrast  to  the  smooth,  clear  appearance  of 
the  cell  contents  for  cultures  with  the  more  favorable  temperatures 
for  enlargement.  The  granulation  was  frequently  pronounced  and 
refraction  was  such  as  to  give  the  whole  hypha  a  very  dense  appearance. 

With  the  lowest  maintained  temperature  tested  (7.5°  C.)  the  hyphal 
diameter  for  Pythiacystis  and  Phytophthora  was  much  greater  than 
with  temperatures  within  the  favorable  temperature  range.  The 
hyphal  contents  for  these  low-temperature  cultures  was  only  slightly 
granular.  The  low-temperature  filaments  of  Pythiacystis  were  much 
swollen  and  were  divided  into  many  short,  thick,  club-shaped  branches  ; 
those  of  Phytophthora  showed  a  series  of  swollen  joints.  These  low- 
temperature  cultures  of  Phomopsis  showed  filaments  somewhat  smaller 
in  diameter,  with  less  frequent  branching,  than  those  of  cultures  grown 
with  favorable  temperatures  for  rapid  enlargement.  In  Diplodia  the 
diameters  of  the  hyphae  were  also  somewhat  smaller  at  7.5°  C.  than  at 
more  favorable  temperatures  for  enlargement. 


THE  EXPERIMENTAL  DATA 

As  previously  noted,  the  temperature  apparatus  contained  a  bat- 
tery of  seven  chambers,  so  that  seven  different  maintained  temperatures 
could  be  employed  at  one  time  for  a  given  series  of  cultures.  After 
preliminary  tests  the  apparatus  was  so  adjusted  as  to  give  the  main- 
tained temperatures  that  promised  to  be  most  useful.  Two  diameters 
of  each  mycelial  disk  were  measured  at  the  end  of  each  24-hour  period 
during  the  experiment.  The  average  of  these  two  measurements  was 
taken  to  represent  the  average  diameter  for  a  given  culture  at  the 
time  of  measurement.  From  this  average  diameter  at  the  end  of  the 
first  24-hour  period  the  diameter  of  the  transplanted  cutting  (2.5  mm.) 
was  subtracted  and  the  remainder  was  taken  as  the  value  for  the 
increment  of  enlargement  for  this  first  observation  period.  The 
difference  between  the  average  measurement  for  the  end  of  the  first 
and  that  for  the  end  of  the  second  24-hour  period  represented  the 


200  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

increment  of  enlargement  for  the  second  24-hour  period.  Increments 
for  the  subsequent  periods  were  obtained  in  a  similar  way.  All  the 
culture  averages  for  a  group  of  like  cultures  in  the  same  chamber 
were  finally  averaged  to  give  the  group  mean.  These  group  means 
were  taken  as  relative  measures  of  the  rates  of  radial  enlargement  for 
the  different  fungi,  different  time  periods,  and  different  maintained 
temperatures. 

In  tables  I-IV  are  presented  the  group  means  for  the  four  fungi, 
for  the  different  maintained  temperatures,  and  for  the  different  24- 
hour  observation  periods,  as  well  as  for  the  first  2-day  and  the  first 
3-day  periods.  In  cases  where  a  considerable  number  of  data  are  at 
hand  for  culture  periods  longer  than  three  days  the  group  means  are 
given  for  the  first  4-day,  first  5-day,  etc.,  period  after  inoculation.  The 
number  of  cultures  employed  in  the  derivation  of  these  group  means 
is  also  indicated  in  each  case  in  parentheses.  The  rates  given  in  tables 
I-IV  do  not  always  represent  single  series.  In  many  cases  the  same 
maintained  temperature  was  tested  at  different  times  for  the  same 
fungus,  and  all  the  measurements  available  for  any  fungus  and  tem- 
perature have  been  used  in  deriving  the  mean  rate  for  that  fungus 
and  temperature,  without  reference  to  the  particular  series  of  tests 
in  which  any  group  of  measurements  may  have  occurred.  Also,  the 
data  in  any  vertical  column  of  these  tables,  representing  the  enlarge- 
ment rates  for  the  respective  maintained  temperatures  indicated  in  the 
first  column,  do  not  all  represent  the  same  series. 

Thus  a  test  for  a  given  maintained  temperature  may  have  been 
made  in  July  and  repeated  in  August  and  the  two  sets  of  data  com- 
bined for  the  particular  fungus  and  temperature  in  question.  Many 
repetitions  of  this  sort  were  made,  involving  the  same  maintained 
temperature  in  different  experimental  series,  and  the  growth  rates  of 
similar  cultures  in  different  series  usually  agreed  as  closely  as  did 
those  of  duplicate  cultures  of  the  same  series.  This  indicated  that 
the  initial  fungus  materials  and  nutrient  medium  used  did  not  ap- 
preciably alter  during  the  period  of  the  investigation.  It  will  be 
noticed  that  the  number  of  cultures  (shown  in  parentheses)  after 
each  rate  in  the  first  part  of  the  tables  usually  decreases  after  the 
second  or  third  consecutive  exposure  period.  This  is  due  to  the  fact 
that  some  of  the  cultures  in  each  temperature  chamber  were  trans- 
ferred to  other  chambers  with  a  different  temperature  after  the  second 
or  third  day,  and  the  subsequent  growth  increments  measured.  These 
data  are  intended  for  a  later  paper  and  are  not  included  in  the  present 
discussion. 


1921]   Faivcett:  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      201 


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1921]   Fawcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      203 


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204  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


TABLE  IV 

Mean  24-Hourly  Diameter  Increments   (mm.)  of  Mycelial  Disks  for 
dlplodia  natalensis 

(Numbers  in  parentheses  indicate  number  of  cultures  from  which  mean  was 

obtained.) 


Maintained 

temperature, 

deg.  C. 

First 
24-hour 
period 

Second 
24-hour 
period 

Third 
24-hour 
period 

7.5 

.OS 

►  (10) 

1.9  (10) 

2.1  (10) 

13.5 

8.0 

(10) 

11.0  (10) 

10.0  (10) 

15.5 

10.1 

(   6) 

13.7  (  6) 

14.2  (   6) 

18.5 

13.0 

(12) 

17.5  (12) 

18.5  (12) 

19.5 

15.5 

(  8) 

20.5  (  8) 

18.5  (  8) 

21.5 

17.0 

(  8) 

21.5  (   7) 

23.5  (   7) 

23.0 

18.2 

(22) 

24.0  (22) 

23.7  (22y 

25.0 

23.0 

(10) 

27.2  (17) 

26.0  (17) 

27.5 

25.9 

(18) 

31.0  (18) 

26.1  (18) 

29.5 

27.7 

(  9) 

29.3  (  9) 

24.5  (  9) 

30.0 

30.0 

(12) 

29.8  (12) 

23.6  (12) 

31.0 

29.3 

(   7) 

25.5  (   9) 

21.5  (  9) 

32.5 

27.5 

(   7) 

25.0  (   7) 

21.1  (   7) 

34.0 

26.0 

(  8) 

21.5  (  8) 

18.0  (  8) 

35.5 

14.5 

(10) 

5.0  (10) 

0(10) 

36.5 

9.1 

(15) 

1.0  (15) 

0(15) 

40.0 

1.5 

(15) 

0(15) 

0(13) 

41.0 

.7 

(  8) 

0(  8) 

0(  8) 

45.0 

.2 

(10) 

0(10) 

0(10) 

First 
2-day 
period 

First 
3-day 
period 

.97 

1.35 

9.5 

9.66 

11.9 

12.66 

15.25 

16.33 

18.0 

18.16 

19.25 

20.66 

21.1 

21.96 

25.1 

25.4 

28.45 

27.66 

28.5 

27.16 

29.9 

27.8 

27.4 

25.43 

26.25 

24.53 

23.75 

21.83 

9.75 

6.5 

5.05 

3.36 

.7 

.5 

.35 

.23 

.1 

.06 

DISCUSSION  OF  RESULTS 

General  Considerations 

It  is  obvious  from  an  examination  of  the  data  in  tables  I-IV  that 
the  magnitude  of  the  mean  rate  of  enlargement  of  mycelial  disks 
(here  expressed  for  convenience  in  terms  of  the  diameter  increment 
per  time  period  of  24  hours)  is  influenced  by  the  variations  in  at  least 
three  conditions  for  any  one  organism,  namely,  (1)  the  degree  of 
maintained  temperature,  (2)  the  length  of  the  time  period  considered 
in  deriving  the  mean  rates,  and  (3)  the  time  relation  of  any  given 
observation  period  to  the  beginning  of  the  entire  culture  period.  As 
has  been  pointed  out,  each  number  in  the  first  column  represents  a 
given  temperature  nearly  constantly  maintained  over  the  entire  period 
indicated  in  1lie  tables.  The  diameter  increments  given  in  the  re- 
maining columns  may  be  considered  as  rates,  expressed  in  millimeters 
per  24  hours  or  one  day.     In  the  first  part  of  the  tables  the  rates  of 


1921]   Faivcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      205 

diameter  increment  (mm.  per  24  hours)  for  any  one  temperature  are 
for  consecutive  exposure  periods,  also  of  24  hours  in  length,  the  con- 
secutive columns  representing  the  manner  in  which  the  increment  rates 
change  from  one  24-hour  period  to  the  next,  etc.,  with  the  lapse  of 
time.  In  this  case  each  exposure  period  has  a  different  time  relation 
to  the  initial  moment  of  exposure  to  the  given  temperature,  i.e.,  each 
exposure  period  began  where  the  preceding  period  terminated.  In 
the  second  part  of  the  table  the  consecutive  columns  show  the  mean 
daily  increments  (mm.  per  24  hours)  for  exposure  periods  of  different 
length  (2  to  6  days),  but  each  having  the  same  time  relation  to  the 
beginning  of  the  culture  period,  the  time  period  always  beginning 
with  the  beginning  of  the  culture  period.  The  rates  derived  in  the 
manner  shown  in  the  second  part  of  the  tables  are  here  included  in 
order  to  show  the  manner  in  which  the  relation  between  growth  and 
temperature  has  been  worked  out  in  some  of  the  previous  investigations 
with  plants  in  which  minimum,  optimum,  and  maximum  temperatures 
for  growth  have  been  considered.  It  was  in  connection  with  the  em- 
ployment of  such  time  periods  as  these  that  Lehenbauer  (1914)  dis- 
cusses the  growth-temperature  relations  for  shoots  of  maize  seedlings. 
It  is  readily  seen  from  an  examination  of  these  tables  that  because 
of  the  influence  of  the  time  factor  the  old  conception  of  a  definite 
optimum  temperature  for  growth  of  a  given  organism  is  inadequate. 
Blackman  (1905)  pointed  out  that  the  term  "optimum  temperature" 
as  commonly  used  had  no  definite  meaning.  Lehenbauer,  in  order  to 
make  the  term  "optimum  temperature"  usable,  defined  it  as  that 
temperature  at  which  there  is  best  growth  during  a  given  time  period. 
In  this  sense  a  process  may  have,  not  one,  but  a  large  number  of  tem- 
perature optima.  Blackman  states  in  connection  with  his  discussion 
of  carbon  dioxide  assimilation  that  the  time  factor  is  important  only 
at  higher  temperatures,  the  higher  the  temperature  the  more  rapid 
the  falling  off  of  the  rate  with  time.  A  new  definition  of  optimum 
temperature,  based  on  this  idea,  has  been  proposed  by  Leitch  (1916), 
namely,  the  highest  temperature  at  which  no  time  factor  enters.  Since 
the  time  factor  may  be  operative  at  all  temperatures  at  which  growth 
is  possible  for  some  organisms,  the  optimum  so  defined  would  have 
no  important  meaning  for  such  organisms.  For  convenience  of  dis- 
cussion, Lehenbauer 's  definition  will  be  followed  in  this  paper.  An 
added  restriction,  however,  is  to  be  placed  on  this  definition  when  the 
growth  rates  for  consecutive  observation  periods  are  to  be  considered. 
An  examination  of  the  first  part  of  tables  I-IV  shows  that  in  order 


206  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

to  define  the  optimum  for  such  data  not  only  must  the  length  of  the 
observation  period  be  stated  but  the  relation  of  that  time  period  to 
the  beginning  of  the  culture  period  must  also  be  given.  Lehenbauer  's 
observation  periods,  from  which  his  rates  were  derived,  all  had  the 
same  relation  to  the  beginning  of  the  culture  period. 

Turning  again  to  the  first  part  of  table  I-IV,  it  is  evident  that 
there  are  three  variables  to  be  considered.  The  growth  rate,  expressed 
in  millimeters  per  24  hours;  temperature,  expressed  in  centigrade  de- 
grees, and  time,  expressed  in  number  of  days  from  the  beginning  of 
the  culture  period.  The  relation  between  these  three  varying  quan- 
tities can  best  be  discussed  for  our  purpose  by  means  of  graphs  and 
the  graphs  used  will  be  of  three  kinds :  ( 1 )  those  showing  the  relation 
between  growth  rate  and  temperature  at  fixed  time  periods,  (2)  those 
showing  the  relation  between  growth  rate  and  the  march  of  time  from 
the  beginning  at  given  maintained  temperatures  of  the  culture,  and 
(3)  those  showing  the  relation  of  the  magnitude  of  the  temperature 
coefficient  (Q10)  to  the  shifting  of  the  10-degree  temperature  intervals 
from  which  the  coefficients  are  derived. 

The  relations  of  these  three  variables  (rate  of  growth,  temperature, 
and  time)  could,  of  course,  all  be  represented  graphically  together  by 
means  of  lines  on  a  drawing  showing  three  dimensions,  as  is  done  by 
Rahn  (1916)  for  rate  of  development  of  bacteria  with  temperature 
and  time.  While  this  is  the  most  complete  manner  of  showing  the 
relation  existing  between  these  three  variables,  making  clear  at  once 
the  uselessness  of  considering  any  growth-temperature  relation  with- 
out reference  to  the  influence  of  time,  it  is  not  so  convenient  for  our 
present  discussion  as  is  the  use  of  a  number  of  simple  graphs. 

The  Growth-Temperature  Graphs 

The  growth-temperature  graphs  were  constructed  in  the  ordinary 
way.  For  the  given  fungus  and  observation  period  the  mean  24-hour 
rates  (first  part,  table  I-IV)  were  plotted  as  ordinates  and  the  indices 
of  maintained  temperature  were  plotted  as  abcissas.  After  the  points 
were  in  place  a  smoothed  graph  was  drawn  in  the  regular  manner. 

To  illustrate  this  process  of  smoothing,  the  four  graphs  for  the 
second  24-hour  period  after  inoculation  are  shown  together  in  figure  I. 
The  points  shown  on  or  near  each  smoothed  graph  represent  the  mean 
rates  taken  from  the  table.  It  is  at  once  seen  that  they  arrange  them- 
selves  in  a  very  satisfactory  manner  as  regards  the  smoothed  graph, 


1921]   Fawcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      207 

i.e.,  that  the  process  of  smoothing  introduces  only  very  slight  alter- 
ations from  any  of  the  values  derived  directly  from  observations. 
These  four  second-day  graphs  are  representative  of  the  others.  All 
are  shown  (without  the  points,  the  values  for  which  may,  however, 
be  obtained  from  tables  I-IV)  in  figures  2-5,  each  figure  presenting 


i 

\ 

/ 

\ 

/ 

\ 

/ 

•  \. 

/ 

\ 

/• 

\ 

Temperature         24 


26         28         30         32 


Fig.  1.  Smoothed  growth-temperature  graphs  for  the  second  24-hour 
period  for  each  of  the  four  fungi  employed.  The  points  represent  the 
actual  increments  as  given  in  tables  I-IV. 

Phythiacystis  citrophthora 

Phytophtliora  terrestria 

Diplodia  vatalensis — 

Phomopsis    citri 

the  several  smoothed  graphs  for  a  single  fungus.  These  graphs  repre- 
sent the  growth-temperature  relations  for  each  one  of  the  successive 
24-hour  observation  periods  (within  the  exposure  period)  for  which 
adequate  data  were  available. 

In  general  form  and  shape  the  growth-temperature  graphs  of  the 
four  fungi  are  much  alike.  Beginning  with  the  lowest  temperature 
tested,  the  graphs  all  rise  gradually,  being  slightly  concave  upward 


208 


University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


at  first,  but  becoming  decidedly  convex  upward  as  the  graph  maximum 
is  approached.  Beyond  this  maximum  region  the  graphs  descend  rap- 
idly to  the  graph  minimum  (maximum  temperature  for  growth).  It 
is  clear  that  the  growth  optimum  always  lies  far  above  (to  the  right  of) 
the  middle  of  the  total  temperature  range  and  that  the  upward  slope 
of  every  graph  is  much  less  steep  than  the  downward  slope. 

In  these  general  characteristics  these  graphs  resemble  those  of  Ed- 
gerton  (1915)  for  the  growth  of  Glomerella,  those  of  Lehenbauer 
(1914)  for  the  growth  of  maize  seedlings,  those  of  Leitch  (1916)  for 
the  growth  of  roots  of  Pisum  sativum,  and  those  of  most  other  students 


2.    Smoothed  growth-temperature  graphs  for  each  of  the  first  five 
24-hour  observation  periods,  for  'Pythiacystis. 

First 

Second    

Third 

Fourth - 

Fifth  


I'i: 


W 

8  10        12  14  16         18         Temperature       24         26         28         30         32  34         36 

3.     Smoothed  growth-temperature  graphs  for  each  of  the  first  five 
24-hour  observation  periods,  for  Pythophthora. 

First   

Second — 

Third 

Fourth 

Fifth 


1921]   Fawcett :  Temperature  Eelations  of  Growth  in  Certain  Parasitic  Fungi      209 

of  life-process-temperature  relations  based  on  short  time  and  temper- 
ature intervals.  The  graphs  published  by  Brooks  and  Cooley  (1917) 
showing  the  relations  of  growth  of  a  number  of  apple  rot  fungi  to 
temperature  for  5-degree  intervals  also  suggest  the  same  general  type 
of  curve. 


5    2 


24         26         28         30 


6  R  10         12         14         16  18       Temperature 

Fig.  4.     Smoothed  growth-temperature  graphs  for  each  of  the  first  five 
24-hour  observation  periods,  for  Phomopsis. 

First 

Second : 

Third 

Fourth 

Fifth 


10  12  14  16         18         20         22       Temperature  28         30         32  34         36  38        40  42 


Fig.  5.    Smoothed  growth-temperature  graphs  for  each  of  the  first  three 
24-hour  observation  periods,  for  Diplodia. 


First  - 
Second 
Third 


210  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


Changes  in  the  Growth-Temperature  Eelations 

The  four  fungi  all  show  very  different  growth-temperature  graphs 
for  the  successive  observation  periods.  For  the  same  fungus  the  mean 
growth  rate  for  any  one  of  the  successive  24-hour  periods  within  the 
entire  exposure  period  is  generally  not  the  same  as  that  for  any  other 
24-hour  period.  It  follows  from  this  that  the  growth-temperature 
graph  for  each  organism  alters  its  shape  as  we  proceed  from  one 
observation  period  to  another  in  the  continuous  series,  as  is  clear  from 
a  superficial  inspection  of  figures  2-5.  This  progressive  change  in  the 
form  of  the  growth-temperature  graph,  of  course,  represents  a  corre- 
sponding progressive  change  in  the  growth-temperature  relation  of 
the  fungus,  as  time  elapses  after  inoculation.  Since  the  external  con- 
ditions of  these  experiments  are  considered  as  not  altering  with  time, 
this  apparently  gradual  change  in  the  growth-temperature  relation 
must  be  evidence  of  internal  physiological  changes  occurring  in  the 
organism. 

When  the  curves  for  the  successive  24-hour  periods  for  each  fungus 
(figs.  2-5)  are  compared  certain  general  features  can  be  noted.  For 
every  fungus  there  is  a  shifting  of  the  apparent  maximum  temper- 
ature for  growth  downward  (to  the  left  in  the  graphs)  with  each 
successive  observation  period.  This  shifting  is  much  more  pronounced 
between  the  first  and  second  24-hour  periods  than  between  any  other 
two  consecutive  periods,  except  in  case  of  Phytophthora.  For  Pythia- 
cystis  the  maximum  shifts  from  about  36°  for  the  first  24-hour  period 
to  about  31°  for  the  fifth  period;  for  Phytopthora  the  corresponding 
displacement  is  from  about  38°  to  about  35°  ;  for  Diplodia  the  maxi- 
mum temperature  changes  from  about  46°  for  the  first  24-hour  period 
to  about  35°  for  the  third  period.  The  maximum  temperatures  for 
Phomopsis  are  more  uncertain. 

A  similar  displacement  of  the  apparent  temperature  optimum 
(graph  maximum)  is  shown  for  all  the  fungi  excepting  Phomopsis. 
The  apparent  optimum  temperature  for  Pythiacystis  shifts  from  about 
27.5°  for  the  first  day  to  about  24°  for  the  fifth  day,  the  corresponding 
change  for  Phytophthora  is  from  about  34°  to  about  28°,  and  for 
Diplodia  the  optimum  is  displaced  from  about  31°  for  the  first  day 
to  about  27°  for  the  third  day. 

Aside  from  the  shifting  of  the  apparent  maximum  and  optimum 
temperature  values  just  considered  it  should  be  noted  that  a  similar 


1921]   Fawcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      211 

displacement  is  evident  for  growth  rates  lying  within  a  large  part  of 
the  suboptimal  region  of  the  growth-temperature  graphs  for  each  fun- 
gus. Throughout  a  large  portion  of  this  suboptimal  region  the  ordi- 
nate value  for  any  given  maintained  temperature  is  greater  for  every 
observation  period  after  the  first  than  it  is  for  the  immediately  pre- 
ceding period.  This  statement  is  true  for  Pythiacystis  for  the  first 
five  24-hour  periods  after  inoculation  and  for  maintained  temperatures 
up  to  21°  C.  It  is  true  for  Phytopthora  and  Phomopsis  for  the  first 
Hive  observation  periods  for  maintained  temperatures  up  to  23.5°  and 
26°  C.  respectively.  For  Diplodia  it  is  true  for  the  first  three  24 -hour 
periods  and  for  maintained  temperatures  up  to  about  21°  C.  In  much 
of  the  supraoptimal  region,  on  the  other  hand,  the  value  of  any  given 
ordinate  value  is  usually  less  than  that  for  the  next  preceding  period. 
The  result  of  these  shiftings  in  the  specific  relations  of  growth  rate 
to  maintained  temperature  is  that  the  growth-temperature  graph  for 
each  successive  observation  period  intersects  the  next  preceding  graph. 
The  only  apparent  exception  to  this  statement  is  for  two  of  the  graphs 
for  Phomopsis,  for  the  third  and  fourth  24-hour  periods.  These  rela- 
tions to  time  are  brought  out  more  clearly  in  graphs  of  figures  8  and  9. 


Growth-Temperature  Relations  of  Different  Organisms  Compared 
by  Means  of  Graphs  of  Equal  Height 

To  compare  the  curvatures  of  different  graphs  it  is  convenient  to 
express  all  the  ordinate  values  of  each  in  terms  of  thje  maximum  and 
to  replot  the  graphs  using  the  values  thus  derived.  This  treatment 
removes  apparent  differences  in  curvature  due  to  differences  in  the 
magnitudes  of  the  maximum  ordinates.  Such  relative  graphs,  for  the 
second  24-hour  observation  period  for  each  fungus,  are  presented  in 
figures  6  and  7.  The  upward  and  downward  slopes  of  these  four 
graphs  are  strictly  comparable  as  to  direction  or  angle,  always  with 
reference,  not  to  actual  growth  rates  in  millimeters,  but  to  relative 
growth  rates,  in  terms  of  the  corresponding  maximum  rate. 

Referring  to  figures  6  and  7,  the  relative  degrees  of  steepness  of 
the  four  graphs  are  nearly  the  same  for  the  suboptimal  region  and 
the  same  is  true  for  the  supraoptimal  region,  except  that  the  graph 
for  Diplodia  is  here  somewhat  less  steep  than  are  the  other  three. 
While  the  actual  values  are  here  hidden,  the  relative  values  as  com- 
pared with  the  maximum  growth  may  be  compared  for  any  process. 
The  four  graphs  differ  considerably  in  other  details,  however,  mainly 


212 


University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


in  regard  to  total  temperature  range  and  in  regard  to  minimum, 
optimum,  and  maximum  temperature  values. 

Since  all  the  graphs  are  brought  to  the  same  height  by  this  treat- 
ment, the  growth-temperature  relations  as  a  whole  for  one  organism 
may  be  compared  more  directly  with  another  irrespective  of  differ- 
ences in  actual  growth  increments.  By  this  means  the  form  of  the 
growth-temperature  graphs  of  a  rapidly  growing  fungus,  for  example, 


1.0- 

*•*■ 

- 

■N 

\ 

0.9- 
0.8- 
0.7. 

/ 

/ 

/ 

/ 

/ 

y 

\ 
\ 

\ 
\ 

0.6- 
0.5. 

/            / 

/ 

/ 

\ 
\ 

0.4. 

/             / 
/              / 

\ 

0.3- 

/            / 
/           / 

\ 

0.2. 

\ 

0.1. 

0,0 

/                S 

/--"                                        '        V 

6  fl  10         12  14  16  18       Temperature        24         26         28  30         32  34         36  38 

Fig.  6.  Growth-temperature  graphs  for  Phythiacystis  and  Phytophthora 
for  the  second  24-hour  period  after  inoculation,  the  ordinate  values  being 
expressed  in  terms  of  the  corresponding  maximum  growth  rate  taken  as 
unity  in  each  case. 

Pythiacystis  citrophthora 

Phytophthora  terrestria 


1.0 
0.9 

0.8 

s 

/, 

/, 

//* 

\ 

0.7. 

/? 

\      \ 
\        \ 
\         \ 

0.6- 

V 

// 

V 

\          \ 

0.5. 

'/ 

/ 

\          \ 

\           \ 
\           \ 

0.4 

y 

' 

0.3 

/ 

/ 

s 

0.2. 

// 

/ 

V 

\          \ 

0.1 

/ ,, 

\          \ 

0.0 

\         \ 

18       Temperature        24 


28        30 


Fig.  7.  Growth-temperature  graphs  for  Phomopsis  and  Diplodia  for 
the  second  24-hour  period  after  inoculation,  the  ordinate  values  being 
expressed  in  terms  of  the  corresponding  maximum  growth  rate  as  unity 
in  each  case. 


Diplodia  natalensis 
I'liomopsis   citri 


1921]   Fawcett :  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      213 

may  be  compared  directly  with  those  of  a  slow-growing  one,  or,  further- 
more, the  rate  of  one  kind  of  a  process  as  influenced  by  temperature 
may  be  compared  with  the  rate  of  any  other  process  no  matter  how 
diverse  or  in  what  units  each  may  be  expressed. 

It  is  to  be  noted  that  if  the  entire  graph  for  Phytophthora  were 
moved  to  the  left  through  4  degrees  of  temperature,  e.g.,  if  all  the 
rates  for  this  fungus  were  plotted  at  temperatures  4  degrees  lower, 
this  graph  would  follow  closely  the  curve  for  Pythiacystis,  except 
that  the  first  part  of  the  downward  slope  is  a  little  steeper  for  .Phy- 
tophthora. The  difference  between  the  two  curves  is,  therefore,  mainly 
one  of  location  of  the  temperature  range  and  the  actual  values  of  the 
increments.  The  extent  of  the  temperature  range,  in  number  of  de- 
grees, and  the  values  of  the  increments  in  relation  to  each  other  and 
to  that  for  the  optimum  are  nearly  the  same  for  these  two  fungi.  The 
growth-temperature  curves  for  the  other  two  fungi,  Phomopsis  and 
Diplodia,  show  the  optimum  temperature  close  to  the  same  point,  27° 
and  28°  C.  respectively.  The  maximum  temperatures  for  these  two, 
however,  appear  to  be  about  33°  for  Phomopsis  and  37°  for  Diplodia, 
a  difference  of  4  degrees. 

TABLE  V 

Characteristics  of  the  Graphs  of  Figures  6  and  7  for  Bates  Equal  to  or 
Greater  Than  0.1  of  the  Maximal  Rate 


Name  of  fungus 

Extent  of 
range  in 
Deg.  C. 

Lower  limit 
of  range 
Deg.  C. 

Upper  limit 
of  range 
Deg.  C. 

Approximate 

optimum  temp. 

Deg.  C. 

Per  cent  of 

range  below 

optimum  temp. 

Pythiacystis 

23.2 

8.7 

31.9 

26.5 

77.7 

Phytophthora 

24.1 

12.0 

36.1 

31.5 

80.5 

Phomopsis 

22.3 

9.1 

31.4 

27.0 

80.2 

Diplodia 

27.6 

8.4 

36.0 

28.0 

72.0 

The  total  ranges  of  temperature  can  not  be  satisfactorily  read 
from  these  graphs,  although  they  are  indicated  in  a  general  way. 
Since  the  interest  of  this  discussion  centers  mainly  about  the  forms 
of  the  graphs  for  the  regions  where  the  mean  24-hour  rates  are  con- 
siderable, the  range  between  the  two  temperatures  giving  a  relative 
rate  of  one-tenth  of  the  maximum  rate  may  be  considered  instead  of 
the  total  temperature  range.  This  range  is  expressed  as  the  length 
of  the  horizontal  line  lying  between  the  two  sides  of  the  graph  and 
having  the  constant  ordinate  0.1.  The  graphs  may  be  compared  with 
respect  to  the  magnitude  of  this  partial  range  and  also  with  respect 
to  the  relative  position  of  the  optimum  temperature  within  this  range. 
The  main  characteristics  of  the  four  graphs  of  figures  6  and  7  are 
shown  in  table  V. 


214  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

The  extent  of  the  temperature  ranges  for  rates  equal  to  or  greater 
than  0.1  of  the  maximum  rate  for  the  four  fungi  are  all  considerably 
different;  Diplodia  has  the  greatest  range  (27.6°)  and  Phomopsis  the 
smallest  (22.3°).  This  partial  temperature  range  has  its  lower  limit 
lowest  (8.4°)  for  Diplodia,  a  little  higher  for  Pythiacystis  (8.7°)  and 
Phomopsis  (9.1°),  and  highest  for  Phytophthora  (12°).  But  the 
four  fungi  do  not  stand  in  this  relation  in  regard  to  the  upper  limit 
of  this  range,  for  Phytophthora  and  Diplodia  show  about  the  same 
limit  (36.1°  and  36°),  while  Pythiacystis  and  Phomopsis  also  nearly 
agree  in  this  respect  (31°  and  31.4°),  the  value  for  the  last  two  being 
markedly  lower  than  for  the  first  two.  Roughly  speaking,  it  may  be 
said  that  from  about  70  to  about  80  per  cent  of  the  temperature  range 
here  considered  lies  below  the  optimal  temperature,  with  from  about 
30  to  about  20  per  cent  lying  above.  Of  course,  such  comparisons  as 
these  might  be  instituted  between  different  fungi  with  reference  to 
any  other  time  period  than  the  one  here  employed ;  only  the  mean 
rates  of  enlargement  for  the  second  24-hour  period  after  inoculation 
are  here  considered. 


Relation  of  Growth  Rate  to  the  Time  of  Exposure 

It  has  been  emphasized  that  the  growth  rates  as  measured  in  the 
work  here  reported  differ  not  only  for  different  fungi  with  the  same 
maintained  temperature  and  for  different  maintained  temperatures 
with  the  same  fungus,  but  also  for  different  consecutive  observation 
periods  with  the  same  fungus  and  the  same  maintained  temperature, 
and  it  has  also  been  pointed  out  that  these  last  differences  in  growth 
rate  must  be  regarded  as  due  to  progressive  alterations  in  the  internal 
conditions  of  the  fungus  as  the  culture  becomes  older. 

This  influence  of  time  on  rate  of  growth  is  best  shown  by  the  set  of 
graphs  shown  in  figures  8  and  9.  Here  the  ordinates  are  in  terms  of 
diameter  increase,  but  the  abcissas  represent  successive  24-hour  periods 
after  exposure  to  a  given  temperature.  Each  graph  shows  growth 
on  successive  days  at  a  given  maintained  temperature. 

Inspection  of  tables  I-IV  and  the  graphs  (figures  8  and  9)  shows 
that  the  mean  rate  of  enlargement  alters  with  the  age  of  the  culture  in 
three  general  ways.  (1)  For  lower  temperatures  the  rate  increases 
throughout  the  culture  period,  the  rate  of  increase  being  generally 
greatest  for  the  first  two  days  and  much  more  gradual  afterwards. 
(2)  For  a  small  range  of  higher  temperatures  the  rate  first  increases 


1921]   Fawcett :  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      215 


Days    1 


Fig.  8.  Graphs  showing  relation  of  rate  of  enlargement  to  age  of 
culture,  for  Pythiacystis  grown  with  various  maintained  temperatures. 
Ordinates  are  24-hour  increments  and  abscissas  are  number  of  days  from 
moment  of  inoculation. 


Days 


Fig.  9.     Graphs   showing  relation  of  rate  of  enlargement  to   age  of 
culture,  for  Phytophthora  grown  with  various  maintained  temperatures. 


216  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

and  then  remains  constant  or  oscillates  till  the  end  of  the  culture 
period.  (3)  For  the  highest  temperatures  with  which  growth  pro- 
ceeds the  rate  decreases  throughout  the  culture  period,  this  decrease 
soon  bringing  the  value  of  the  growth  rate  to  zero. 

These  graphs  which  indicate  roughly  the  change  of  rate  with  time 
at  various  maintained  temperatures  suggest  that  we  may  have  here  a 
family  of  curves,  which  if  the  data  were  sufficient  would  be  capable 
of  mathematical  treatment.  It  may  be  seen  from  tables  I  to  IV  and 
graphs  of  figures  8  and  9  that  in  general  the  rates  increased  with  the 
time  at  temperatures  below  about  20°  C.  For  example,  with  Pythia- 
cystis  the  upper  limit  was  about  19.5°  C.  and  with  Phythophthora  it 
was  about  21.5°  for  the  6  days  tested.  The  growth  rate  in  general 
decreased  with  time  from  the  second  day  and  thereafter  at,  and  above, 
about  30°  C.  With  Pythiacystis  it  was  at  or  above  27.5°  C.  and  with 
Pythophthora  at  or  above  30°  C.  These  same  effects  are  apparent  in 
some  of  the  graphs  showing  the  relation  of  temperature  to  the  growth 
of  apple  rot  fungi  published  by  Brooks  and  Cooley  (1917). 

That  the  increase  or  decrease  in  growth  rate  with  lapse  of  time 
in  the  present  study  was  not  due  to  the  accumulation  of  products  in 
the  yet  unused  portions  of  the  medium  was  shown,  at  least  for  Pythia- 
cystis, by  special  tests  in  which  fresh  medium  was  placed  at  the  ad- 
vancing edges  of  parts  of  the  mycelial  disks  after  they  had  grown 
for  two  days.  The  subsequent  rate  of  advance  of  the  mycelial  disk 
upon  the  fresh  medium  at  the  various  maintained  temperatures  was 
the  same  as  that  upon  the  remainder  of  the  unoccupied  medium  that 
had  been  in  the  dishes  from  the  start. 


1921]   Fawcett:  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      217 


TEMPERATURE  COEFFICIENTS 

Introductory. — A  temperature  coefficient  as  here  considered  may 
be  denned  as  the  ratio  of  the  rate  of  a  given  process  at  any  given 
temperature  to  the  rate  at  another  temperature  at  a  fixed  interval 
below  the  first  temperature.  While  the  temperature  interval  consid- 
ered may  have  any  magnitude  desired,  it  has  been  usual  to  consider 
in  most  chemical  and  physiological  studies  an  interval  of  10  degrees 
centigrade.  In  some  investigations,  where  the  rate  considered  alters 
greatly  for  small  differences  of  maintained  temperature,  temperature 
coefficients  for  smaller  intervals  have  been  used. 

The  temperature  coefficient  for  the  rate  of  any  process  for  a  dif- 
ference of  10  degrees  is  frequently  represented  by  the  symbol  Q10. 
When  derived  directly  from  experimental  data  showing  rates  for  tem- 
perature intervals  of  10  degrees  this  coefficient  is,  of  course,  the  quo- 
tient obtained  by  dividing  the  rate  for  the  higher  temperature  by  the 
rate  for  the  lower.  It  is,  however,  frequently  calculated  from  data 
at  irregular  temperature  intervals.  The  values  obtained  from  such 
data  by  the  employment  of  the  usual  formulae  appear  to  be  reliable 
only  when  the  coefficient  is  constant,  or  nearly  so,  over  a  considerable 
range  of  temperature.  Where  the  coefficient  is  changing  rapidly  with 
successive  intervals  of  temperature,  as  is  the  case  in  many  physio- 
logical processes,  such  derived  coefficients  are  apt  to  be  misleading. 

Temperature  coefficients  for  physiological  processes  have  been  much 
discussed  in  the  literature.  The  statement  occurs  in  numerous  papers 
that  the  rate  of  a  certain  process  under  consideration  does,  or  does 
not,  obey  the  ' '  Van 't  Hoff-Arrhenius  rule ' '  for  chemical-reaction  veloc- 
ities with  change  in  temperature,  this  rule  being  commonly  under- 
stood to  mean  that  the  reaction  velocity  is  continuously  doubled  or 
trebled  for  each  rise  of  10  degrees  centigrade.  It  has  been  usual  for 
some  biologists  and  chemists  to  use  this  rule,  as  thus  understood,  to 
decide  whether  a  given  process  should  be  regarded  as  chemical  or 
physical  in  its  nature.  If  the  rate  of  the  process  in  question  be  found 
to  have  a  10-degree  temperature  coefficient  lying  between  2  and  3, 
this  is  often  considered  an  indication  that  the  process  dealt  with  is  a 
chemical  one  or  is  controlled  by  chemical  reactions.  If,  on  the  other 
hand,  the  10-degree  temperature  coefficient  proves  to  be  much  below  2, 


218  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

this  is  taken  as  an  indication  of  a  physical  reaction.  In  many  dis- 
cussions of  temperature  influence  on  process  rates  it  has  been  assumed 
that  if  this  coefficient  appears  to  be  more  or  less  nearly  constant  for 
several  10-degree  ranges  and  has  a  magnitude  between  2  and  3  for 
the  particular  ranges  studied,  then  the  process  follows  the  Van 't  Hoff- 
Arrhenius  rule.  If,  on  the  other  hand,  the  coefficient  be  not  constant 
with  higher  and  lower  10-degree  ranges,  but  varies  greatly  above  3 
or  below  2,  it  is  considered  that  the  rule  does  not  hold.  This  common, 
narrow  interpretation  of  the  Van't  Hoff-Arrhenius  rule  appears  to 
have  been  based  on  a  general  misconception  of  the  Van't  Hoff  formula. 
It  has  been  clearly  pointed  out  by  Stuart  (1912)  that  Van't  Hoff's 
formula  itself  makes  clear  that  a  constant  coefficient  is  not  implied 
even  for  chemical  reactions  and  that  Van't  Hoff  (1896)  himself  recog- 
nized that  the  coefficient  values  of  different  10-degree  ranges  are  by 
no  means  to  be  taken  as  constant ;  they  are  generally  smaller  with 
higher  10-degree  ranges  and  larger  with  lower  ones.  All  that  Van't 
Hoff  did  was  to  make  a  very  rough  generalization  and  to  point  out 
that  in  many  chemical  reactions  within  the  temperature  usually  dealt 
with  in  experimental  observations  it  was  interesting  to  note  that  the 
temperature  coefficient  was  apt  to  fall  between  2  and  3.  If  it  is  not 
usual  for  the  temperature  coefficient  to  be  constant  for  simple  chemical 
reactions,  it  is  not  to  be  expected  that  it  would  be  constant  for  physio- 
logical processes,  where  much  more  complex  reactions  take  place.  An 
examination  of  the  experimental  data  on  the  relation  of  a  large  number 
of  life-processes  to  temperature  shows  that  the  temperature  coefficients 
for  such  processes  generally  tend  to  diminish  in  value  from  lower  to 
higher  ranges  of  temperature.1  Kanitz  (1905)  appears  to  have  been 
one  of  the  first  to  regard  this  feature  as  an  essential  in  the  analysis 
of  the  relationship  between  rates  of  life-processes  and  maintained 
temperatures. 

Trautz  and  Volkmann  (1908)  gave  considerable  attention  to  this 
variation  in  the  magnitudes  of  the  temperature-coefficients  for  certain 
chemical  processes,  and  Snyder  (1911)  pointed  out  that  since  it  is  the 
rule  for  the  temperature  coefficients  of  chemical  reactions  to  vary  with 
temperature  such  variation  should  be  expected  in  physiological  pro- 
cesses. Livingston  (1916)  noted  that  the  temperature  coefficient  of 
the  growth  rates  of  maize  seedlings,  as  determined  by  Lehenbauer 
(1914),  might  be  regarded  as  following  the  Van't  Hoff  rule,  as  com- 
monly understood,   only  for  a  very  limited  range  of  temperatures. 


i  Data  for  a  large  number  of  life-process  rates,  with  citations  of  363  papers, 
have  been  collected  and  compiled  in  a  monograph  by  Kanitz  (1915). 


1921]   Faivcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      219 

Leitch  (1916),  using  short  exposure  periods,  found  that  for  the  growth 
of  Pisum  sativum  the  temperature  coefficient  (Q10)  decreased  grad- 
ually from  8.25  for  the  interval  between  0°  and  10°  C.  to  2.2  between 
18°  and  28°  C.  The  coefficients  given  by  Lehenbauer  (1914)  for 
maize  seedlings  decrease  from  6.56  for  the  10-degree  interval  between 
12°  and  22°  C.  to  1.88  for  the  interval  between  22°  and  32°  C.  Rahn 
(1916),  taking  his  data  from  experiments  of  Marshall  Ward  (1895) 
on  the  rate  of  development  of  Bacillus  ramosus  and  B.  coli,  constructed 
some  curves  of  the  temperature  coefficients,  showing  how  these  decrease 
rapidly  from  high  values  for  low  temperature  intervals  to  low  values 
for  higher  temperature  intervals.  Matthaei's  (1905)  data  for  the  rate 
of  carbon  assimilation  with  temperature,  from  which  Blackman  de- 
rived the  temperature  coefficient  of  2.1,  show  that  the  coefficient  varied 
greatly  even  at  the  lower  ranges,  where  the  time  factor  was  least  oper- 
ative, from  a  high  value  for  the  lowest  intervals  to  a  much  lower  value 
for  higher  intervals.  Moore's  (1918)  work  with  the  influence  of  tem- 
perature on  the  rate  of  heart  beat  of  Fundulus  embryo  shows  that 
the  temperature  coefficient  decreases  progressively  from  7.6  at  the 
temperature  interval  2.5°  to  12.5°  C.  to  1.4  for  the  interval  25°  to 
35°  C.  Denny  (1916),  reviewing  the  monograph  by  Kanitz  (1915) 
on  temperature  and  life  processes,  says : 

' '  Many  processes  in  living  organisms  show  a  temperature  coefficient 
approximately  that  of  the  Van't  Hoff  law  (2  to  3)  within  certain 
limits.  Among  the  plant  processes  for  which  this  has  been  found  to 
be  the  case  the  following  may  be  mentioned:  C02  assimilation  (Mat- 
thaei)  between  0°  and  37°  C. ;  respiration  of  seedlings  (Kuijper)  be- 
tween 0°  and  35°  C. ;  geotropic  presentation  time  (Rutgers)  between 
5°  and  25°  C. ;  phototropic  presentation  time  (M.  S.  De  Vries)  be- 
tween 5°  and  25°  C. ;  protoplasmic  streaming  in  Elodea  (Velton)  be- 
tween 2.5°  and  35°  C. ;  permeability  of  plant  cells  and  tissue  (Ryssel- 
berghe)  between  0°  and  30°  C. ;  intake  of  water  by  barley  grains 
(Brown  and  Worley)  between  3.8°  and  34.6°  C." 

An  examination  of  the  data  in  most  of  these  cases  will 'show  that 
while  the  coefficients  are  of  the  order  of  magnitude  required  by  the 
so-called  "Van't  Hoff  rule,"  in  a  majority  of  cases  there  is  (even 
within  the  limited  range  to  which  the  rule  is  supposed  to  apply)  a 
marked  tendency  for  them  to  decrease  from  lower  to  higher  intervals 
of  temperature ;  so  that  one  may  conclude  that  even  these  coefficients 
form  part  of  a  coefficient-temperature  curve  which  if  extended  to  the 
left  would  approach  infinity  and  if  extended  to  the  right  would  arrive 


220  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

at  zero.  The  temperature  coefficients  given  by  Loeb  and  Chamberlain 
(1915)  for  the  rate  of  segmentation  of  Arbacia  decrease  from  6  for 
a  temperature  interval  between  8°  and  18°  C.  to  2.5  between  15° 
and  25°  C. 

Temperature  Coefficients  in  the  Present  Study. — The  growth-tem- 
perature relations  of  the  four  fungi  used  in  the  work  here  reported 
were  studied  in  certain  aspects  by  means  of  such  temperature  co- 
efficients as  have  just  been  considered.  Since  unexplained  fluctuations 
in  growth  rate  as  related  to  temperature  are  to  be  neglected,  it  being 
desired  to  obtain  information  of  a  general  nature  only,  the  mean  24- 
hour  rates  for  the  various  24-hour  observation  periods  ( given  in  tables 
I-IV)  were  not  employed  in  calculating  the  coefficients.     Instead  of 

TABLE  VI 

Mean   24-Hour  Bates  of  Enlargement  for  Consecutive   1-Day   Observation 

Periods,  for  Pythiacystis,   as  Determined  by  Measuring  the 

Ordinates  of  the  Smoothed  Graphs  of  Figure  2 


Temperature 
deg.  C. 

First  day 
mm. 

Second  day 
mm. 

Third  day 
mm. 

Fourth  day 
mm. 

Fifth  day 
mm. 

8 

.3 

.8 

.9 

1.1 

1.4 

9 

.5 

1.2 

1.4 

1.6 

2.0 

10 

.7 

1.7 

1.9 

2.2 

2.4 

11 

1.0 

2.3 

2.5 

2.8 

3.1 

12 

1.3 

2.9 

3.0 

3.4 

3.7 

13 

1.6 

3.5 

3.6 

4.0 

4.2 

14 

2.0 

4.1 

4.3 

4.7 

5.0 

15 

2.4 

4.8 

5.0 

5.4 

5.8 

16 

2.8 

5.5 

5.7 

6.2 

6.5 

17 

3.3 

6.2 

6.5 

6.8 

7.2 

18 

3.7 

6.8 

7.1 

7.5 

8.0 

19 

4.2 

7.4 

8.0 

8.3 

8.7 

20 

4.7 

8.0 

8.7 

8.9 

9.2 

21 

5.1 

8.6 

9.3 

9.5 

9.7 

22 

5.7 

9.1 

9.8 

9.9 

10.0 

23 

6.1 

9.6 

10.2 

10.3 

10.2 

24 

6.6 

9.9 

10.4 

10.5 

10.3 

25 

7.1 

10.2 

10.4 

10.4 

10.1 

26 

7.6 

10.4 

10.3 

10.2 

9.9 

27 

8.0 

10.4 

10.1 

9.8 

9.5 

28 

8.1 

10.2 

9.6 

9.3 

8.8 

29 

7.8 

9.4 

8.7 

8.3 

7.9 

30 

7.1 

7.8 

7.4 

6.9 

6.4 

31 

6.1 

5.3 

3.5 

1.5 

.5 

32 

4.8 

.7 

0 

0 

0 

33 

2.6 

0 

34 

.9 

35 

.4 

36 

0 

1921]   Fawcett:  Temperature  Belations  of  Growth  in  Certain  Parasitic  Fungi      221 

these,  the  length  of  the  ordinate  for  each  degree  on  each  of  the  smoothed 
graphs  of  figures  2-5  were  used.  These  ordinate  values  are  presented 
in  tables  VI-IX.  The  arrangement  and  notation  of  the  first  parts  of 
tables  I-IV  are  here  followed. 

From  these  ordinate  values  of  the  smoothed  growth-temperature 
graphs  were  calculated  temperature  coefficients  for  every  10-degree 
interval  by  whole  degrees,  between  the  lowest  and  highest  maintained 
temperatures  tested  for  each  of  the  consecutive  24-hour  observation 
periods  represented  in  tables  VI-IX.  To  illustrate  the  method  fol- 
lowed, the  mean  24-hour  growth  rate  for  Pythiacystis  for  the  first 
day  after  inoculation  is  seen  to  be  0.3  mm.  for  a  maintained  temper- 
ature of  8°  and  3.7  mm.  for  a  maintained  temperature  of  18°  C.    The 

TABLE  VII 

Mean  24-Hour  Eates  of  Enlargement  for  Consecutive   1-Day  Observation 

Periods,   for  Phytophthora,   as   Determined   by   Measuring   the 

Ordinates  of  the  Smoothed  Graphs  of  Figure  3 


Temperature 
deg.  C. 

First  day 
mm. 

Second  day 
mm. 

Third  day 
mm. 

Fourth  day 
mm. 

Fifth  day 
mm. 

8 

.07 

.25 

.4 

1.0 

1.1 

9 

.15 

.4 

.9 

1.5 

1.6 

10 

.2 

.7 

1.2 

2.0 

2.1 

11 

.3 

1.0 

1.7 

2.5 

2.7 

12 

.5 

1.4 

2.2 

3.0 

3.3 

13 

.7 

1.9 

2.7 

3.5 

3.9 

14 

.9 

2.4 

3.3 

4.1 

4.5 

15 

1.1 

3.0 

3.9 

4.7 

5.2 

16 

1.4 

3.7 

4.5 

5.3 

5.8 

17 

1.7 

4.4 

5.3 

5.9 

6.5 

18 

2.0 

5.2 

6.0 

6.6 

7.2 

19 

2.4 

6.0 

6.7 

7.2 

7.9 

20 

2.7 

6.9 

7.4 

7.9 

8.6 

21 

3.0 

7.8 

8.2 

8.7 

9.3 

22 

3.3 

8.6 

9.0 

9.3 

9.9 

23 

3.6 

9.3 

9.8 

10.1 

10.3 

24 

4.0 

10.0 

10.5 

10.7 

10.7 

25 

4.3 

10.8 

11.1 

11.3 

10.9 

26 

4.6 

11.4 

11.8 

11.9 

11.1 

27 

5.0 

11.9 

12.3 

12.4 

11.3 

28 

5.3 

12.5 

12.8 

12.9 

11.3 

29 

5.7 

12.9 

13.2 

13.3 

11.3 

30 

6.0 

13.3 

13.4 

13.6 

11.2 

31 

6.4 

13.5 

13.6 

13.7 

11.0 

32 

6.7 

13.5 

13.6 

13.6 

10.7 

33 

6.9 

12.2 

12.8 

12.6 

9.2 

34 

7.1 

9.5 

11.2 

10.2 

6.0 

35 

6.1 

5.7 

6.8 

4.2 

1.0 

36 

2.2 

1.7 

.5 

.2 

222  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

ratio  3.7  :  0.3  is  12.3,  which  is  the  10-degree  coefficient  (Q10)  for  the 
10-degree  interval  from  8°  to  18°  C.  Now,  since  the  value  of  Q10 
varies  with  the  maintained  temperature,  if  its  fluctuations  are  to  be 
studied  it  is  necessary  to  calculate  the  different  values,  not  for  suc- 
cessive 10-degree  intervals  (as  8°-18°,  18°-28°,  28°-38°),  but  for  10- 
degree  ranges  beginning  with  each  successive  whole  degree  for  which 
data  are  available  (as  8°-18°,  9°-19°,  10°-20°,  etc.).  If  the  value 
just  obtained  for  the  range  8°-18°  C.  be  written  Q10  (8°-18°)  =12.3, 
then  referring  to  table  VI  we  may  write  Q10  (9°-19°)  =8.4;  Q10 
(10°-20°)  =  6.7  ;  Q10  (11°-21°)  =  5.1,  etc.  For  convenience  of  ref- 
erence and  for  facility  in  plotting  these  temperature  coefficients  for 
various  10-degree  temperature  ranges  as  they  are  made  to  shift  by 
single  degrees,  the  middle  point  of  each  10-degree  range  is  taken  to 
represent  the  range  itself.  Thus  the  coefficient  value  plotted  at  13° 
stands  for  the  10-degree  temperature  coefficient  for  the  range  (8°-18°) 
whose  middle  point  is  13°  (figs.  10  and  11). 

TABLE  VIII 

Mean  24-Hour  Eates  of  Enlargement  for  Consecutive,  1-Day  Observation 

Periods,  for  Phomopsis,  as  Determined  by  Measuring  the 

Ordinates  of  the  Smoothed  Graphs  of  Figure  4 


Temperature 
deg.  C. 

First  day 
mm. 

Second  day 
mm. 

Third  day 
mm. 

Fourth  day 
mm. 

Fifth  day 
mm. 

8 

.1 

.4 

1.1 

1.2 

1.3 

9 

.2 

.7 

1.4 

1.5 

1.6 

10 

.3 

1.1 

1.8 

1.8 

2.0 

11 

.4 

1.4 

2.1 

2.1 

2.4 

12 

.5 

1.9 

2.4 

2.5 

2.8 

13 

.6 

2.2 

2.8 

2.9 

3.2 

14 

.8 

2.6 

3.1 

3.2 

3.6 

15 

1.0 

3.0 

3.5 

3.6 

4.0 

16 

1.2 

3.4 

3.9 

4.0 

4.4 

17 

1.4 

3.7 

4.2 

4.4 

4.8 

18 

1.6 

4.1 

4.6 

4.8 

5.2 

19 

1.8 

4.5 

5.0 

5.2 

5.6 

20 

2.1 

4.9 

3.4 

5.7 

6.1 

21 

2.3 

5.3 

5.8 

6.1 

6.5 

22 

2.6 

5.8 

6.2 

6.5 

7.0 

23 

3.0 

6.2 

6.6 

7.0 

7.4 

24 

3.4 

6.7 

7.1 

7.4 

7.8 

25 

3.8 

7.1 

7.5 

7.8 

8.2' 

26 

4.1 

7.5 

7.8 

8.2 

8.4 

27 

4.4 

7.7 

7.9 

8.5 

8.3 

28 

4.2 

7.4 

7.8 

8.2 

8.0 

29 

3.4 

6.0 

7.0 

7.6 

7.3 

30 

2.4 

3.0 

5.0 

6.6 

5.8 

31 

1.5 

1.2 

1.2 

3.3 

1.8 

32 

.9 

.3 

.2 

1921]   Faivcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      223 

The  10-degree  coefficient  values  for  all  whole  intervals  of  10  degrees 
for  which  data  are  at  hand  for  all  four  fungi  and  for  each  of  the 
successive  24-hour  observation  periods  employed  in  this  experimenta- 
tion are  set  forth  in  table  X.  The  first  column  of  this  table  presents 
the  different  temperature  ranges,  the  second  column  shows  the  middle 


TABLE  IX 

Mean  24-Hour  Bates  of  Enlargement  for  Consecutive  1-Day   Observation 

Periods,  for  Diplodia,  as  Determined  by  Measuring  the  Ordinates 

of  the  Smoothed  Graphs  of  Figure  5 


Temperature 
deg.  C. 

First  day 
mm. 

Second  day' 
mm. 

Third  day 
mm. 

8 

.7 

2.7 

3.0 

9 

2.0 

4.1 

4.5 

10 

3.2 

5.6 

5.8 

11 

4.4 

7.0 

7.2 

12 

5.7 

8.4 

8.7 

13 

6.8 

9.9 

10.1 

14 

8.1 

11.3 

11.7 

15 

9.3 

12.7 

13.1 

16 

10.5 

14.1 

14.6 

17 

11.8 

15.7 

16.1 

18 

13.1 

17.0 

17.6 

19 

14.3 

18.5 

18.9 

20 

15.6 

20.0 

20.5 

21 

17.0 

21.6 

22.2 

22 

18.4 

23.0 

23.5 

23 

19.8 

24.5 

24.7 

24 

21.2 

26.1 

25.4 

25 

22.7 

27.6 

26.0 

26 

24.2 

29.1 

26.3 

27 

25.8 

30.5 

26.3 

28 

27.2 

30.8 

25.8 

29 

28.8 

30.5 

24.9 

30 

29.7 

29.2 

23.8 

31 

29.7 

27.4 

22.6 

32 

29.0 

25.6 

21.0 

33 

27.4 

23.0 

19.0 

34 

24.9 

12.0 

15.9 

35 

19.9 

11.0 

9.3 

36 

11.4 

2.7 

37 

7.4 

38 

5.0 

39 

3.0 

40 

1.5 

41 

.8 

42 

.5 

43 

.4 

44 

.3 

45 

.2 

224 


University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


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1921]   Fawcett:  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      225 

points  of  these  ranges,  which  are  to  be  taken  as  representing  the 
various  ranges  themselves.  The  rest  of  the  table  falls  into  four  parts, 
each  part  giving  the  data  for  a  single  fungus.  Each  single  column 
gives  the  coefficients  for  a  single  one  of  the  consecutive  24-hour  ob- 
servation periods. 

Inspection  of  the  coefficient  values  given  in  table  X  brings  out 
the  fact  that,  for  every  one  of  the  four  fungi  and  for  each  of  the 
consecutive  24-hour  observation  periods,  the  10-degree  temperature 
coefficient  for  mycelial  enlargement  is  greatest  for  the  lowest  temper- 
ature shown  and  regularly  decreases  toward  higher  temperatures,  be- 
coming smallest  for  the  highest  temperatures.  The  highest  coefficient 
value  here  encountered  (30)  is  that  for  13°  C.  (range  from  8°  to  18°), 
for  the  first  24  hours  after  inoculation,  for  Phytophthora.  This  value 
is  progressively  smaller  for  progressively  higher  temperatures,  becom- 
ing 0.47  for  the  temperature  31°  (range  from  26°  to  36°).  For  the 
temperature  13°  (range  from  8°  to  18°)  the  lowest  coefficient  value 
shown  (4.0)  is  for  the  fourth  24-hour  period  for  Phomopsis,  and  this 
value  is  progressively  smaller  for  progressively  higher  temperatures, 
becoming  0.5  for  the  temperature  26°  (range  from  21°  to  31°).  The 
lowest  coefficient  value  of  the  whole  table  is  0.01,  for  the  temperature 
31°  (range  from  26°  to  36°)  for  the  fourth  24-hour  period  for  Phy- 
tophthora, this  value  being  progressively  larger  with  progressively 
lower  temperatures  and  becoming  6.6  for  the  temperature  13°  (range 
from  8°  to  18°). 

Aside  from  the  regular  falling  off  in  the  coefficient  value  for  each 
observation  period  and  fungus,  as  we  pass  from  lower  to  higher  tem- 
peratures, as  just  pointed  out,  the  value  for  any  temperature  and 
fungus  is  always  largest  for  the  first  24-hour  period  after  inoculation 
and  generally  tends  to  become  smaller  with  each  successive  period 
after  the  first,  although  this  last  statement  is  not  always  strictly  true 
for  all  temperature  ranges.  The  relation  of  the  value  of  this  temper- 
ature coefficient  to  the  maintained  temperature  representing  the  middle 
point  of  the  10-degree  temperature  range  from  which  each  coefficient 
value  is  derived  is  shown  graphically  for  the  second  24-hour  period 
after  inoculation,  for  three  of  the  fungi  in  figure  10.  Abscissas  rep- 
resent these  middle  points,  while  ordinates  are  the  corresponding  co- 
efficient values.    These  graphs  have  not  been  smoothed. 

These  three  graphs  of  10-degree  temperature  coefficients  are  seen 
to  be  alike  in  their  general  form.  Every  one  begins  with  a  relatively 
very  high  value  at  the  left   (lowest  temperature  range  tested)   and 


226 


University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 


descends,  rapidly  at  first  and  then  less  rapidly,  with  higher  temper- 
atures. 

From  the  nature  of  the  temperature  coefficient  it  is  clear  that  its 
value  for  any  range  of  maintained  temperatures  having  its  lower  limit 
just  below  the  minimum  temperature  for  enlargement  must  be  infinite, 
since  the  ratio  of  any  positive  quantity  to  zero  is,  of  course,  infinity. 

On  the  other  hand,  as  the  temperature  range  for  which  the  co- 
efficient value  is  calculated  has  its  upper  limit  approaching  the  maxi- 
mum temperature  for  enlargement  the  coefficient  value  approaches 
zero.    No  matter  what  range  of  temperature  is  employed,  a  change  of 


13  14  15   16  17  18   19  20  21  22  23  24   25  26  21     28  29  30  31  32 

Fig.  10.  Graphs  of  the  10-degree  temperature  coefficient,  as  related  to 
temperature,  for  Phytophthora,  Pythiacystis  and  Diplodia,  for  the  second 
24-hour  period  after  inoculation. 


1921]   Faiccett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      227 

maintained  temperature  from  some  value  below  the  maximum  temper- 
ature to  some  value  above  that  cardinal  point  must  be  accompanied 
by  a  corresponding  change  in  the  rate  of  enlargement  from  a  positive 
value  to  zero,  and  the  ratio  of  zero  to  any  positive  quantity  is,  of 
course,  zero. 

For  graphs  such  as  those  here  considered  it  follows  (from  the 
points  brought  out  above)  that  the  slope  of  the  graph  at  the  point  of 
maximum  ordinate  value  (left  end)  appears  to  furnish  a  criterion  by 
which  it  may  be  judged,  at  least  in  a  general  way,  how  nearly  the 
abscissa  of  this  point  approaches  the  minimum  temperature.  An 
inspection  of  the  curves  at  the  lowest  temperature  range  here  consid- 
ered (8°-18°  C.)  indicates  that  its  lower  limit  (8°  C.)  is  much  more 
nearly  the  minimum  temperature  for  enlargement  for  Phytophthora 
than  it  is  for  the  other  fungi.  The  curves  also  indicate  that  8°  is 
nearer  the  temperature  minimum  for  Pythiacystis  than  for  Diplodia. 

Since  the  graph  of  temperature  coefficient  as  related  to  temperature 
shows  ordinates  that  decrease  in  magnitude  from  infinity  to  zero,  it 
follows  that  there  must  be  some  point  on  every  such  graph  at  which 
the  ordinate  value  is  unity.  This  point  at  which  the  temperature  co- 
efficient value  is  unity  will  represent  the  middle  point  of  a  range 
within  which  lies  the  optimum  temperature.  The  temperature  value 
corresponding  to  this  abscissa  is,  therefore,  near  the  temperature 
optimum  for  the  process  considered.  For  lower  temperatures  the  co- 
efficient values  are  all  greater  than  unity,  for  higher  ones  they  are  all 
smaller  than  unity. 

A  point  that  needs  emphasis  in  studying  the  general  nature  of  the 
temperature  coefficients  of  most  processes  showing  temperature  minima 
and  maxima  is  this,  that  every  such  process  must  show  a  certain  tem- 
perature range  for  which  the  temperature  coefficient  has  values  be- 
tween 2.0  and  3.0,  etc.  It  is,  therefore,  quite  without  any  definite 
meaning  to  state  that  the  temperature  coefficient  for  any  process  has 
a  certain  value,  unless  the  corresponding  temperature  range  is  simul- 
taneously stated.  The  coefficient  value  may  be  everything  between 
zero  and  infinity,  depending  on  the  temperature  range  considered  and 
upon  the  position  of  that  range  within  the  total  temperature  range 
of  the  process.  The  so-called  Van't  Hoff  rule,  stating  that  the  temper- 
ature coefficients  of  many  chemical  reaction  velocities  have  values 
between  2.0  and  3.0  is  obviously  true,  therefore,  if  the  proper  temper- 
ature ranges  are  considered.  It  appears  to  be  true  that  many  simple 
chemical  reactions  and  many  physiological  processes  show  temperature 


228  University  of  California  Publications  in  Agricultural  Sciences        [Vol.  4 

coefficient  values  between  2.0  and  3.0  for  certain  temperature  ranges 
within  the  ordinary  range  of  weather  temperatures  on  the  earth,  and 
it  is  perhaps  this  fact  that  has  led  to  so  much  inadequate  discussion 
about  these  coefficients,  especially  in  physiological  literature.  Great 
emphasis  should  be  placed  upon  the  fact  that  the  temperature  co- 
efficient for  most  processes  having  temperature  limits  is  a  continuously 
varying  value,  the  variation  proceeding  from  infinity  to  zero. 

From  this  point  of  view  the  temperature  relations  of  different 
processes  under  stated  non-temperature  conditions  and  with  stated 
exposure  periods  are  clearly  comparable,  not  by  means  of  single  tem- 
perature coefficient  values,  but  by  means  of  the  coefficient-temperature 
relation  as  a  whole.  Practically,  the  simplest  way  to  present  this  re- 
lation for  a  given  process  is  to  construct  such  coefficient-temperature 
graphs  as  those  shown  in  figures  10  and  11.  The  form  and  position  of 
these  graphs  completely  describe  the  rate-temperature  relation.  If  two 
processes  are  to  be  compared  in  respect  to  this  temperature  relation,  the 
comparison  should  be  instituted  between  the  two  coefficient-temperature 
graphs,  constructed  on  the  same  scale.  If  the  two  graphs  coincide 
throughout,  then  the  temperature  relations  of  the  two  processes  are 
alike;  they  have  approximately  the  same  temperature  minima,  op- 
tima, and  maxima,  and  the  two  rates  change  from  one  temperature 
to  another  in  just  the  same  way.  If  the  two  graphs  fail  to  coincide 
throughout,  the  two  rate-temperature  relations  differ,  and  just  how 
they  differ  is  apparent  from  an  inspection  of  the  graphs.  Further- 
more, the  different  values  of  the  temperature  coefficient  for  the  same 
process,  etc.,  may  readily  be  compared  for  different  temperatures  and 
the  coefficient  values  for  different  processes  may  be  compared  for  the 
same  temperatures.  Some  of  the  points  brought  out  by  inspection  of 
the  group  of  three  coefficient-temperature  graphs  shown  in  figure  10 
have  been  mentioned,  but  many  others  not  here  considered  may  be 
noted. 

The  three  graphs  thus  far  dealt  with  show  the  relation  of  temper- 
ature coefficients  to  temperature  for  three  of  the  fungi  employed  in 
this  study  and  for  the  second  24-hour  period  after  inoculation.  The 
four  coefficient  graphs  for  Pythiacystis,  for  the  first,  second,  third, 
and  fourth  24-hour  periods  after  inoculation,  are  shown  in  figure  11. 
These  graphs  are  constructed  from  the  data  given  in  table  X  in  the 
manner  employed  for  figure  10;  they  have  not  been  smoothed.  The 
graph  for  each  successive  period  after  the  first  lies  below  the  one  for 
the  preceding  period.    The  progressive  lowering  (already  mentioned) 


1921]   Fawcett:  Temperature  Eelations  of  Growth  in  Certain  Parasitic  Fungi      229 

of  minimum,  maximum,  and  optimum  temperatures  with  the  succes- 
sive periods  is  clearly  shown ;  also  the  difference  between  the  growth- 
temperature  relation  for  the  first  period  and  that  for  the  second  is 
shown  to  be  far  more  pronounced  than  all  the  differences  between 
these  relations  for  successive  periods. 


13      14     15     16     17    18     19     20     21     22     23    24     25      26   27     28     29    30 


Fig.  11.  Graphs  of  the  10-degree  temperature  coefficient,  as  related  to 
temperature,  for  Pythiacystis,  for  four  consecutive  24-hour  observation 
periods  within  the  4-day  exposure  period. 


CONCLUSION 

From  the  results  of  the  investigation  of  the  temperature  relations 
of  growth  in  pure  cultures  of  four  fungi  (Pythiacystis  citrophthora, 
Pliytophthora  terrestria,  Phomopsis  citri,  and  Diplodia  natalensis) , 
discussed  in  detail  in  the  preceding  pages,  the  following  generalizations 
may  now  be  brought  together. 

It  was  indicated  that  there  is  the  usual  optimum  temperature  above 
and  below  which  the  rate  of  enlargement  was  smaller  with  higher  or 
lower  maintained  temperatures.  Growth-temperature  graphs  (with 
temperatures  as  abscissas  and  growth  rates  as  ordinates)  rise  from 
left  to  right  (from  lower  to  higher  temperatures) ,  being  at  first  slightly 
concave  upward,  then  becoming  convex  till  the  optimum  is  passed,  and 
then  falling  rapidly  toward  the  temperature  axis. 

The  fact  is  to  be  emphasized  that  the  optimum  temperature  for 
the  average  rate  of  growth  of  a  given  fungus  with  a  given  medium  is 


230  University  of  California  Publications  in  Agricultural  Sciences        [Vol.4 

not  always  the  same  for  different  lengths  of  observation  periods,  or 
when  periods  of  equal  length  have  different  time  relations  to  the  be- 
ginning of  the  culture  period. 

With  culture  periods  of  from  three  to  six  days  and  an  observation 
period  of  24  hours  in  length,  it  was  found  that  in  general  the  optimum 
temperature  for  growth  shifted  to  lower  temperatures  for  each  suc- 
cessive observation  period.  There  was  also  corresponding  displacement 
of  the  apparent  maximum  temperature  downward  (from  higher  to 
lower  temperatures)  with  each  successive  observation  period. 

A  comparative  study  of  the  growth-temperature  graphs  of  the  four 
fungi  for  the  second  24-hour  period  shows  that  the  total  range  of 
temperature  within  which  growth  rate  values  are  one-tenth  or  more  of 
the  maximum  rate  includes  from  32.5  to  37  centigrade  degrees  of  the 
temperature  scale.  Of  this  range,  from  70  to  80  per  cent  is  below  the 
optimum  temperature  for  growth. 

With  comparatively  low  temperatures  the  growth  rate  increases 
with  the  age  of  the  culture  throughout  the  culture  period  and  with 
the  highest  temperatures  it  decreases  throughout  the  culture  period, 
this  decrease  soon  bringing  the  value  to  zero.  With  a  small  range  of 
intermediate  temperatures,  the  rate  first  increases  with  time  and  then 
remains  constant,  oscillates  or  decreases. 

The  10-degree  temperature  coefficient  (Q10)  for  each  of  the  four 
fungi  has  a  high  value  at  the  lowest  range  studied  and  decreases  pro- 
gressively through  lower  values  to  zero.  The  form  of  the  graphs  repre- 
senting the  value  of  the  temperature  coefficient  as  related  to  different 
ranges  of  maintained  temperature  shows  that  the  value  of  the  temper- 
ature coefficient  must  begin  with  infinity  for  some  low  range,  must 
pass  through  all  finite  values  and  then  must  reach  zero  for  some  higher 
range.  For  growth-temperature  relations  of  this  type  the  range  for 
which  the  coefficient  is  unity  will  include  the  optimum  temperature, 
the  range  for  which  the  coefficient  is  infinity  will  include  the  minimum 
temperature,  and  the  range  for  which  the  coefficient  is  zero  will  include 
the  maximum  temperature. 

The  use  of  the  coefficient-temperature  graphs  furnishes  a  direct 
method  of  comparing  the  growth-temperature  relations  of  different 
organisms,  no  matter  in  what  units  the  rates  have  been  expressed.  If 
the  graphs  of  two  different  processes  coincide  throughout,  the  growth- 
Icinperature  relations  must  be  considered  to  be  the  same.  On  the 
other  hand,  if  the  two  graphs  fail  to  coincide  throughout,  their  lack 
of  coincidence  furnishes  evidence  of  the  particular  manner  in  which 
the  temperature  relations  of  the  two  processes  differ. 


1921]   Fawcett :  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi      231 


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